THE ELECTROLYTIC
DISSOCIATION THEORY
BY
Prof. R. ABEGG, Ph.D.
4i in is idylls
of the University of Breslau
AUTIK
CARL L. von ENDE, Ph.D.
Assistant Professor of Chemistry , State University of Iowa
FIR S T EDITION
FIRST THOUSAND
NEW YORK
JOHN WILEY & SONS
London : CHAPMAN & HALL, Limited
1907
Copyright, 1907,
BY
CARL L. von ENDE
DEDICATED
To My Dear Teacher and Friend
Soante Qlrrljeuitw
The Founder of the Dissociation Theory
TRANSLATOR’S PREFACE.
It seemed worth while to give English readers the
benefit of this account of the electrolytic dissociation theory
at the hand of a master of its details and applications.
I gladly acknowledge my indebtedness, in so many
ways, to my wife in preparing this translation, and also
to Dr. Frederic Bonnet, Jr., of Worcester Polytechnic
Institute, for helpful criticisms and suggestions.
C. L. v. E.
Iowa City, Iowa.
AUTHOR’S PREFACE.
As reasons for acting in place of the founder in pre-
senting the dissociation theory, I may be permitted to
mention the request of the publisher of this collection 1
to undertake the task, and to this I would add the en-
thusiasm which must seize upon every one who has taken
the opportunity to study thoroughly this beautiful theory
and learn how many old problems have been solved by
it at one stroke, and how many new ones have come into
view and been mastered.
Quite recently, Roloff set himself the same task for a
similar class of readers, and it offered some difficulty to
keep this presentation from becoming merely competitive.
I have for that reason touched but briefly upon the
historical development, which is so adequately given by
Roloff, and have endeavored to confine myself more to the
detailed account of the chemical side, particularly to the
development of the equilibrium relations among electro-
lytes. While I believed that Ostwald’s exposition in his
“ Foundations of Analytical Chemistry,” which showed
“ Sammlung chemischer und chemisch-technischer Vortrage,” edited
Prof, ©r, Felix. Ahrens (Ferd. Stuttgart).
vii
AUTHOR'S PREFACE
viii
so clearly the usefulness of the ion theory for every-day
chemical purposes, was sufficient for the initiated, yet
for a deeper insight into this attractive field a fuller account
was desirable. In particular I have laid great stress on
developing the formulae as simply and clearly as possible,
and therefore the proofs have not infrequently been given
in a form differing more or less from those in the original
papers. These modifications have also seemed desirable
as a result of my teaching experience.
There is, of course, no intention of laying claim to new
scientific achievements. We are justified, on the whole,
in considering that Arrhenius himself has so thoroughly
worked over the material that important advances of a
general nature are scarcely to be expected; hence the
nitiated will meet with new ideas and developments in
only a few instances.
Breslau, April, 1903.
CONTENTS.
PAGE
Preface iii, v
Fundamental Conceptions of the Theory x
Mobility of the Ions 29
Equilibria among Ions 37
The Dissociation Constant 46
Equilibria among Several Electrolytes 61
Hydrolysis 76
Avidity 95
Indicators • 100
Heterogeneous Equilibria 105
Anomaly of Strong Electrolytes 121
Influence of Pressure and Temperature on Dissociation. 134
Non-aqueous Solutions 147
Chemical Nature and Ionization Tendency of the
Elements 159
Index. 165
THE THEORY OF
ELECTROLYTIC DISSOCIATION.
FUNDAMENTAL CONCEPTIONS OF THE THEORY . 1
In the year 1887, when the Swedish physicist Svante
Arrhenius propounded the theory of electrolytic disso-
ciation (ionization), physical chemistry was passing from
a kind of attractive side issue to a more central position
of interest among chemists. Very interesting physical
properties had been studied for some time and although
the general laws were discovered, which with Ostwald
we at present summarize under the caption Additive
Properties, yet none of these furthered to any marked
extent the constitution problems then prominent in the
minds of organic chemists. The eyes of chemists were
drawn again to the field of physical chemistry by the
methods (discovered in 1883 by the recently deceased
1 The sign * = positive ionic charge per equivalent, and the sign ' =
negative ionic charge per equivalent. Chemical formulae in parenthesis,
for example (H’)» indicate concentration of the kind of molecule in-
closed, in this instance hydrogen ion..
2 THE THEORY OF ELECTROLYTIC DISSOCIATION .
Frenchman Raoult) for determining molecular weights
by means of freezing- and boiling-points of solutions.
This deter min ation of the molecular weights of substances
in solution was an exceedingly useful aid in all kinds
of chemical investigations. It was only natural, there-
fore, that van’t Hoff’s 1 epoch-making theory of solutions,
which appeared in the transactions of the Swedish
Academy in 1885, and gave at once the theoretical ex-
planation for the laws found by Raoult, should attract
more attention in the chemical world than would have
been possible under other circumstances, especially as it
dealt with nothing less than judging the certainty of the
conclusions based on the molecular-w r eight determina-
tions of Raoult. General attention was further attracted
to physical chemistry by the founding of the u Zeitschrift
fur physikalische Chemie ” by Ostwald, at the beginning
of his activities as a teacher at Leipzig, and by the com-
pletion, shortly before that, of his well-known “ Lehrbuch
der Allgemeinen Chemie,” in which he brought together
and formulated as a whole all physical chemical knowl-
edge.
Through extended studies of his own on the conduc-
tivity of electrolytic solutions, and through the theory
of van’t Hoff as to the state of substances 2 dissolved in
water, Arrhenius was led to look upon the so-called
electrolytes, i.e., the acids, bases, and salts belonging
especially to the field of inorganic chemistry, as broken
up to a definite and usually large extent into their con-
1 See “Sammlung chemischer und chemisch-technischer Vortrage,”
Vol. V.
Mbid.
FUNDAMENTAL CONCEPTIONS OF THE THEORY . 3
stituents, the ions. These ions, provided with electric
charges, conduct the current by moving through the
solution to the electrodes.
This conception of free-existing parts of chemical
molecules was nothing new among physicists. Davy
(1808) and Faraday (1833), in their famous investigations
on the electrolysis of fused and dissolved salts, and
Hittorf, in his studies on the concentration changes caused
by electrolytic conduction, had assumed and made prob-
able such a molecular decomposition, even if such decom-
position were not of very definite extent.
These conceptions gained in significance through the
experimental verifications of Buff (1855) and the theoret-
ical proofs of Clausius (1857) and Helmholtz (1880), which
showed that during electrolysis the components of the
chemical molecules, though moving in opposite directions,
do so without the least consumption of energy . The
seemingly necessary assumption, on the part of chemists,
of an affinity between the part-molecules was thus dis-
proved, and there was no physical reason, therefore, for
not considering the ions as independent of one another,
that is, the molecules split up into such ions. We do not
intend at this place to enter farther into the very inter-
esting history of the subject, a detailed account of which,
it may be well to mention, is to be found in the readable
article of Roloff, 1 but rather to occupy ourselves with a
presentation of the substance of the theory and its suc-
cesses in the field of chemistry.
As the name “electrolytic dissociation” indicates, the
1 Zeitschr. f. angew. Chem., 15 , Heft 22-24 (1902).
4 THE THEORY OF ELECTROLYTIC DISSOCIATION.
theory of Arrhenius includes all those substances which
we term electrolytes, i.e., the substances which conduct
the galvanic current in such a way that a movement of
material masses takes place simultaneously in the direc-
tions of the positive and negative currents. As has long
been known, this peculiar kind of electric conduction is
a property of salts, acids, and bases, and through them of
almost all substances belonging to the field of inorganic
chemistry. As Hittorf showed, we can formulate directly
the statement that electric conduction is the essential
characteristic of those substances known as “ salts” in
the broader sense, and accordingly acids are looked
upon as salts of hydrogen, and bases as salts of hydroxyl.
Hereby a clear conception of “salt” was formulated for
the first time, about which long experience had given us
a practical but nevertheless inexact notion.
In many cases the ions are determined by the nature
of the products which separate at the electrodes during
electrolysis; thus, for example, the ions of the saltCuCl 2
are on the one hand the positive component Cu, separat-
ing at the cathode, and on the other the negative Cl.
Hittorf in his classical researches showed how one can in
general determine the nature of the ions, that is, the com-
ponents wandering in opposite directions, by the shift-
ing of the concentrations which take place during elec-
trolysis. That a salt, such as K2SO4, does not break
up into K 2 0 and SO3, but into K 2 and SO4, is shown
by comparison with KC1, in which Cl is the negative
and therefore K the positive ion; and since both salts
behave alike as to their positive component, having the
K ion in common, the negative component of K 2 S0 4
FUNDAMENTAL CONCEPTIONS OF THE THEORY . 5
must be essentially SO 4, or the residue after taking away
the K.
On this conception as a basis one readily arrives at the
long and vainly sought exact definitions of acids and
bases. While it was sufficiently well known that their
characteristic constituents were H and OH respectively,
nevertheless it had not been possible to define under
what circumstances these components showed acid or
basic properties; for there are numerous compounds
containing H or OH which are not necessarily acids or
bases. The dissociation theory, however, defines these
substances for us as such which contain H or OH in the
'form of ions as the result of electrolytic dissociation, and
makes clear at once the way of informing ourselves as to
the degree of the acid or basic properties of a compound,
by determining the concentration of these characteristic
H" or OH' ions. This will be discussed later.
. Let us here summarize a few of the more characteristic
reactions peculiar to these two most important kinds of
ions.
The H* ions
1. Change the color of u indicators”; for example,
color blue litmus red, methyl orange red,
decolorize red phenolphthalein solution -and
yellow nitrophenol solution, etc.;
2. Hasten catalytically the decomposition of esters
by water into alcohol and acid, the inversion
of cane-sugar, also the hydrolysis of maltose;
3. Act as a solvent on many metals, marble, etc. ;
4. Cause “acid” taste;
6 THE THEORY OF ELECTROLYTIC DISSOCIATION.
5. Neutralize all characteristic properties of OH'
ions.
The OH' ions
1. Change the color of indicators in the reverse
sense of the H‘ ions;
2. Act as saponifiers of esters;
3. Accelerate catalytically the condensation of
acetone to diacetone alcohol (also the reverse
reaction), the conversion of hyoscyamine into
atropine, and the disappearance of multi-
rotation;
4. Neutralize all characteristic properties of H #
ions.
Other ions have their specific reactions as well, but it
is certain that, for reasons as yet unknown, we have to
consider catalytic action as especially belonging to H’
ions and OH' ions, even if it is true that occasionally
other substances can act catalytically.
According to the theory of Arrhenius, these salts must, to
a certain extent, be broken up into their ions, and the most
convincing evidence for this conclusion was his discovery
that all these salts were at the same time such substances
as gave in aqueous solutions, according to the investi-
gations of Raoult, freezing-point depressions which did
not correspond to the molecular weights assumed from
chemical considerations. While many substances dis-
solved in water depress the freezing-point of the water
by 1. 85° for each mole per liter, Raoult found that a
considerable number of substances, particularly when
FUNDAMENTAL CONCEPTIONS OF THE THEORY . 7
dissolved in water, gave greater depressions ; or, according
to the above-mentioned rule, they seemed to contain
in a liter more than one mole, in spite of the fact that
only one gram-molecule of the substance had been used
for solution. Similarly the boiling-points of the same
solutions showed too great a rise, thus urging the same
conclusion. One was thereby brought to face the alterna-
tive, either to doubt on the chemical assumptions the
general tenability of Raoult’s law, or to admit on the
basis of its validity that out of every molecule of these
deviating substances several independent parts are
formed. In assuming the latter the dissociation theory
followed the same line of thought that was so successfully
applied by Cannizzaro, Kopp, and Kekule in explaining
the abnormal vapor densities of such substances as
ammonium chloride, phosphorus pentachloride, and
others. For, according to the van’t Hoff solution theory,
the changes in the freezing- and boiling-points are the
measures of the osmotic pressure of the dissolved sub-
stances, and this osmotic pressure is entirely analogous
to gas pressure.
It is customary to speak of Raoult’s methods as methods
for the determination of molecular weights; it would seem
clearer, however, to call them methods for determin-
ing molecule number or normal concentration, for the
changes in freezing-point and boiling-point give directly
only the number of moles of whatever kind contained in
a definite volume of the solvent. Not until we consider
the amount by weight contained in the solution do we
arrive at the apparent molecular weight, which only
represents a real molecular weight w T hen we can leave
8 THE THEORY OF ELECTROLYTIC DISSOCIATION .
out of consideration the grouping together or splitting up
of individual molecules. Since in so many cases this is
hot* permissible, it is more rational to speak of the the-
oretically unobjectionable molecular concentration given
by the osmotic pressure or the methods of Raoult. The
establishment of the qualitative agreement between the
substances which conduct electrolytically and those which,
according to the methods of determining normal con-
centration, suffer a molecular splitting up was of very
great immediate significance and was evidence supporting
the idea of Arrhenius, for it was only natural to identify
this molecular decomposition with the production of
electrolytically conducting ions. The next consideration
was the finding of a quantitative measure of proof. This
was gained through Arrhenius, who considered that the
degree of the conductivity must represent a measure of
the ionic decomposition, in that the conductivity is
essentially carried on by the ions and must take place
the more readily the more ions are present, or the farther
the electrically inactive molecules are split up into elec-
tricity-transporting particles. Again, the molecular-num-
ber methods (on condition that we look upon the ions as
well as the undissociated molecules as independent indi-
viduals) give a direct measure of the degree of ionic decom-
position, so that the full molecular concentration of such a
salt solution consists of that of its undissociated molecules
increased by that of its ions, van’t Hoff had introduced
a factor i into his theory of solutions, which indicates
the number of times the molecular concentration given
by the osmotic methods is greater than that to be expected
from the chemical formula.
FUNDAMENTAL CONCEPTIONS OF THE THEORY . 9
Indicating by a the fraction of a mole 1 of a salt which
is split up into ions, and by (i — a) the undecomposed
portion, we can calculate the factor i if we know n the
number of ions into which one molecule can break up.
We have then, for i mole, the part (i — a) left undis-
sociated and (n-a) ionic molecules formed from the
rest; the sum total of undissociated and ionic mole-
cules is therefore (i — OL-\-na) individuals, so that
i=i — a-\-na = i + (n — i)a.
A first proof of the theory is given by the fact that a ,
the degree of dissociation, can be derived from the measure-
ment of the conductivity. Under the assumption, which,
as we shall find later, holds for neutral salts, that at very
great dilutions the breaking up of the salt into ions
becomes practically complete, the comparison of the
conductivities produced by one mole of the salt when
dissolved in a definite volume of water with the con-
ductivity it assumes at very great dilution gives the degree
of ionic decomposition. While we shall later consider
in detail the more exact determination of the degree of
dissociation of different substances, let us here anticipate
to the extent of saying that Arrhenius, in the year 1888, 2
in testing on an extended scale the relationship between
i and a , as derived above, found an excellent substan-
tiation of the theory.
A very important question, the solution of which had
occupied chemists in vain for a long time, was this, What
is formed in a mixture of salts? For instance, to what
1 Mole = gram-molecule.
2 Zeitschr. physik. Chem., 2 , 491 (188S).
10 THE THEORY OF ELECTROLYTIC DISSOCIATION .
extent, if at all, does a reaction take place to form K0CO3
and Na2S04 when one mole of K2SO4 and one mole of
Na2C03 are brought together in solution? It is sur-
prising to note that it is by no means generally known
that the solution of the two salts named is identical with
the one obtained by mixing a mole each of K2CO3 and
Na 2 SC>4. The author has repeatedly met chemists who
to this day in all seriousness discuss how the metal and
acid constituents of such a mixture are mutually combined.
The dissociation theory, however, gives for this an
entirely convincing explanation that can readily be tested
at the hand of experience. Since, according to this
theory, K 2 S 0 4 and Na 2 C 0 3 as well as K 2 C 0 3 and
Na 2 S 0 4 are to a large extent split up into the ions K, Na,
S 0 4 , and C 0 3 , it is clear that it can make no difference
from what solid substances these ions take their origin,
for in the solution they have become independent of the
constituent originally combined with them. This con-
sideration is of practical significance, for example, in the
artificial preparation of mineral-water salts which shall
give solutions identical with those of the natural springs . 1
Suppose analysis shows that a certain well-water contains
for 1 equivalent of sulphate 2 equivalents of chlorine, |
equivalent of potassium, and 2 \ equivalents of sodium, it
is absolutely immaterial and leads to exactly the same
solution if we mix \ equivalent K 2 S 0 4 , \ equivalent
Na 2 S 0 4 , and 2 equivalents NaCl, or 1 equivalent Na 2 S 0 4 ,
1 J equivalents NaCl, and \ equivalent KC 1 , or in general
any quantities of the four salts made up of the four
1 Zeitschr. f. Elektrochem., 9 , 185 (1903).
FUNDAMENTAL CONCEPTIONS OF THE THEORY, n
components, provided we meet the condition that the total
amount of K, Na, SO 4, and Cl equals that of the analysis.
This experimental fact may be summed up in the state-
ment that salts are such substances as are in a high
degree subject to a so-called mutual decomposition,
which, and this is of importance, takes place with im-
measurable velocity.
An exceedingly important fact of chemistry and one in
very close relationship with the above is the striking
phenomenon that in practically all salts the basic and
acid components show exactly the same reactions no
matter in what combination these components happen to
be. Thus it is a well-known fact that all soluble barium
salts give with all soluble sulphates one and the same
reaction, that is, form barium sulphate. Similarly
copper is precipitated as copper sulphide by hydrogen
sulphide from all of its salt solutions quite independent of
the acid component with which it is combined; chlorine
gives the same precipitate with silver nitrate no matter
whether it is contained in KC 1 , NaCl, CuCl2, etc., etc.
On the other hand, in the case of organic compounds, the
same radical at times shows greatly varying reactions,
depending on the nature of the other elements combined
with it. Now it seems highly improbable and directly
contradictory to the character of chemical compounds
that different compounds should give an identical reaction
with, the same substance; yet in the case of salts, as we
saw above, we cannot avoid this very conclusion. But
here again the dissociation theory offers the solution of
the dilemma, for, according to its concept, the same radical
in tlie different salts, in consequence of . electrolytic dis-
12 THE THEORY OF ELECTROLYTIC DISSOCIATION.
sociation, appears as a free and, in all cases, equal ion
and therefore gives the same reaction. The entire
structure of analytical chemistry is built up on this fact,
and the especial feature of the system of inorganic analysis
is its relative convenience and simplicity, which is condi-
tioned essentially on the identity of a substance being
maintained in spite of its manifold combinations. On
the contrary, an organic system of analysis must be, to all
intents and purposes, counted with the impossibilities on
account of the infinite diversity of the reactions.
A further peculiarity of a salt solution is the additive
nature of its physical properties, such as color, density,
refractivity, conductivity, and so on. By this we under-
stand that these properties can be made up of two quan-
tities, one of which can be assigned to the base alone, the
other to the acid alone, so that if we know these separate
values for a certain number of radicals, we can calculate
the properties of each combination by simply adding the
corresponding quantities. As a type of the additive
properties of electrolytes we can take that of the chemical
reactions just discussed.
Thus Ostwald 1 established the fact that the character-
istic absorption spectra of equivalent solutions of per-
manganates, for instance, are the same, independent of
the (colorless) cathion with which the Mn0 4 was
combined, that is to say, each ion imparts to the solution
its own peculiar color. For this reason all dilute solutions
containing copper ions are blue, all ferrous salt solutions
greenish, all rosaniline salts red, etc. We may further
g - ' — “ — —
. r
1 physik, Cheni./ 9 , $79 (1893)
FUNDAMENTAL CONCEPTIONS OF THE THEORY. 13
conclude that all ions present in a colorless solution have
no color of their own: as H*, K*, Na*, Li*, Ba**, Sr",
Ca**, Mg**, Be**, OH', F', Cl', Br', I', SO/', N 0 3 ',
CIO/.
Frequently the color can also give interesting informa-
tion as to the constitution of inorganic salts. Thus neither
potassium ferrocyanide nor potassium ferro-oxalate pos-
sesses the green color of the Fe*‘ ion, but they are yellow 7
and red respectively, and hence must contain the Fe
in some other form, that is, as the complex ions Fe(CN)e / ' //
and Fe(C 2 0 4 )2" respectively, as was demonstrated by
Hittorf. Likewise the change in color of Cu" ions by
ammonia, or their decolorization by potassium cyanide,
discloses the fact that complex ions are formed in which
the copper is no longer present as Cu*\ All such con-
clusions have found their remarkable confirmation
experimentally.
Buckingham found 1 that fluorescence is often es-
sentially the property of an ion and is wanting in the
undissociated substance, as in the case of eosine, / 9 -naph-
thylamine disulphonic acid (1:2 :5), and quinine. Here
the ions retain their entirely independent properties.
Further, Valson found that equivalent solutions of
KC 1 and NaCl show a difference in specific gravity,
which remains unchanged when w r e substitute for Cl
any other acid residue, thus indicating that the difference
is independent of the nature of the acid. In the same
way any two acids give a constant difference independent
of the basic constituent. At every hand, then, we have
\ geitschTr physik,- Chein., 14 , 129 (1894),
14 THE THEORY OF ELECTROLYTIC DISSOCIATION .
evidence that the components of electrolytes do not
mutually influence each other.
All these phenomena are to be looked upon as necessary
consequences of the ionic dissociation, .for the properties
of the ions must be constant as long as the ions remain
the same. If therefore the combination of the ions does
not affect their nature, that is, leaves them independent
and free, the additive nature of the properties follows as
a necessity.
A great number of objections have been raised to the
conception that the constituents of “ salts ” in the broader
sense lead a chemical existence independent of one
another. Above all, the opinion had always been held
that the foremost salt-formers, the alkalis on the one hand
and the halogens on the other, were bound one to the
other by extraordinary affinity forces, since they react
with very great affinity manifestations, such as intense
heat liberation and even light. And now would these
components be separated again by simple solution in
water? In asking this, the fact was entirely overlooked
that the dissociation theory does not assume that the
electrolytes split up into the atoms or molecules from which
they were formed, but that these decomposition products
are essentially different from those atoms or molecules,
in that they are electrically charged. These charges are
of enormous magnitude, since, according to Faraday’s
law, each ion carries for its formula weight, in grams,
96580 coulombs per equivalent.
It is also claimed that the abnormal osmotic pressures
of the electrolytes can be explained by a hydrolytic de-
composition— for instance, . NaCI +H 2 0 =NaOH +HCL
FUNDAMENTAL CONCEPTIONS OF THE THEORY. 15
This assumption, however, leads ad absurdum, since, in
the first place, the assumed decomposition products,
NaOH and HC 1 , which in their turn cannot undergo
further hydrolysis, also show, like the salt, too high an
osmotic pressure. And secondly, as has long been
known, solutions of acids and bases, which according
to the assumption of opponents would have to exist
alongside without reacting, on the contrary, do react
with one another very energetically. The theory of
neutralization here involved will be further discussed
later on in the light of electrolytic dissociation.
Another criticism has been the impossibility of applying
to ionic decomposition the crucial experimental test of sep-
arating the decomposition products of the split-up body, as
in the case of the gaseous dissociation of ammonium chlo-
ride. In this it was overlooked that the separating of the
oppositely charged ions cannot take place to a measurable
extent by reason of these very charges, since it would
require the setting free of enormous quantities of elec-
tricity. For should w T e wish to isolate from each other
only one milligram equivalent of cathion and anion, it
would be necessary to have appear, at different points of
the system in space in which this separation was to take
place, electrostatic charges of 96 coulombs. This means
charges of a magnitude sufficient to give to a large flask
provided with a condenser covering, such as was employed
by Ostwald and Nemst, 1 a potential of about 8000 volts!
Nernst, 2 however, showed, in his epoch-making theory
1 Zeitschr. physik. Chem., 3 , 120 (1S89),
’Ibid,, 2 , 01, 3 (:§§§); 4 , i?9 (1889),
l6 THE THEORY OF ELECTROLYTIC DISSOCIATION.
of the diffusion of electrolytes and the so-called diffu-
sion chains, how these local separations of cathions and
anions, even though immeasurably small, do take place,
and can be employed for a quantitative calculation of
these changes. Again, together with Ostwald 1 he
demonstrated, by using two vessels connected with a
siphon filled with an electrolytic acid solution, that it is
possible by means of most powerful electrostatic in-
fluences to transfer a sufficient excess of ions with
positive charges into the one capillary vessel, and nega-
tively charged ions into the other, so that upon conduct-
ing away the excess of electricity in the former the dis-
charged hydrogen ions are made visible as bubbles of
hydrogen gas. Hence this objection can also be
considered as being in every particular effectively refuted.
Likewise another theory, known as the hydrate theory,
attempted to meet the phenomena explained by the theory
of Arrhenius, and in particular to explain the important
phenomenon of the increased osmotic pressure. This
theory states that the molecules of the dissolved sub-
stances combine with considerable quantities of the
water solvent to form hydrates, whereby the molecular
concentration of the dissolved substance, i.e., the ratio
of the number of dissolved molecules to that of the
free uncombined solvent molecules, may appear greatly
increased in that the molecules of solvent consumed for
hydration no longer act as solvent. There is nothing to
be said against the fundamental conception of this theory
of a chemical union between the two components of a
t g^tsch'r. phvsik, Ckem., 3 , 196 (188$).'
FUNDAMENTAL CONCEPTIONS OF THE THEORY . 17
solution; on the contrary, the results of recent and varied
physico-chemical research make it appear more and
more probable. In spite of this the hydrate theory is
incapable of competing from a quantitative standpoint
with the dissociation theory. Since the abnormally high
osmotic pressures also appear in extremely dilute solu-
tions, in fact are most evident there, the hydrate theory
would have to assume, in case of a tuW normal solution
which gives double the normal freezing-point depression,
that, of the approximately 55 moles of water contained
in one liter, about one half, or 27 moles of water at least,
are bound to yioVir mole of the dissolved substance,
giving as a formula for this hydrate 1 mole salt + 2 7000
H 2 0 . Further, it is evident that, in spite of the varying
concentration of the solute, the number of bound water
molecules would always have to remain approximately
constant, provided the abnormality factor i of the osmotic
pressure, as is often actually the case, scarcely varies with
the concentration. This conclusion is altogether contrary
to the law of mass action, according to which the hydrated
portion of the salt must be proportional to the product
of the anhydrous portion and the active mass of the
water, expressed by the equation:
Hydrate = k • (Anhydride) • (Water).
Now on account of thermodynamical reasons (Nemst)
the active mass of water is proportional to its vapor
pressure, and this, according to Raoult’s measurements, is
only about 2% smaller for a normal solution than for
pure water, i.e., for dilute solutions it may be considered
practically identical with that of water, so that the active
1 8 the theory of electrolytic dissociation.
mass of the water in the above equation is -constant;
which means that the quantity of hydrate in such solu-
tions is proportional to the quantity of anhydride. It
follows that the quantity of water bound as hydrate would
have to become less and less with increased dilution of
the solute, and so the abnormalities of the osmotic pressure
noted at greater concentrations would also continually
decrease, which is directly contrary to the observed facts.
But leaving all of this out of the question, the dissociation
theory is capable of giving in an extremely convincing
manner orientation as to the magnitude of the abnormality
factor i according to the number of ions into which an
electrolytic molecule splits up, in that binary salts of the
type of KC 1 can give rise to twice the normal value of the
osmotic pressure, ternary salts such as K 2 S 0 4 or MgCl 2
to three times, and so on. Thus, for instance, we can
read directly from the formula K 4 Fe(CN) c that in
consequence of the decomposition into five ions, 4K and
the anion of the tetrabasic hydroferrocyanic acid, the
maximum molecular osmotic pressure (at greatest dilution)
must be five times the normal; for sodium mcllitate,
which can split up into seven ions, Taylor 1 attained nearly
the maximum value (see table, p. 25). On the other
hand, from the value of the factor i, the hydrate theory
would have to set up an hypothesis as to the degree of
hydration for each particular salt concerned, but this
hypothesis would be encumbered by the previously
mentioned defect. So we can hardly be in doubt as to
which theory to prefer, especially when we consider that
1 Qstwald’s Zeitschr ., 27 , 361 ( 1898 ),
FUNDAMENTAL CONCEPTIONS OF THE THEORY . 19
the hydrate formulae, which it would be necessary to
employ in order to explain the osmotic pressures, do not
in the remotest agree with the known water of crystalliza-
tion formulae, making them seem altogether arbitrary.
Even if we can herewith consider this theory as disposed
of, so far as explaining the fundamental facts of dissocia-
tion is concerned, we shall nevertheless meet the same
again later on (p.127), where for certain anomalies of
electrolytes it offers a possible explanation.
The most prominent problem which the dissociation
theory had to solve — its fundamental concept once accepted
— was the determination of the degree of dissociation of
the different electrolytes. It has been mentioned that
this may be done by means of the abnormality of the
osmotic pressure, by introducing into the calculation the
increase in the number of molecules produced by the ions
formed in extremely dilute solutions, where we may
consider the ionization as complete and the abnormality
factor i must reach its maximum limiting value. This
value at the same time indicates the number of ions that
are formed from the salt molecule.
Another way to get at the degree of dissociation
Arrhenius found in the study of electric conductivity.
The specific conductivity k of an electrolyte is the current
strength which flows when the same is placed between
two electrodes of 1 square centimeter area, 1 centimeter
apart, with a potential difference of 1 volt.
For one and the same electrolyte this specific conduc-
tivity is naturally very much dependent on the concen-
tration, since as it varies, the amount of the electrolyte, con-
tained in the 1 centimeter cubed between the electrodes.
20 the THEORY OF ELECTROLYTIC dissociation.
must vary. The study of the specific conductivity can
therefore give directly no means for finding out in what
way the molecule of the substance changes its capacity
for conducting electricity with varying dilution. Such
a means is gained, however, from the specific conductivity,
if we reduce the same by calculation to one and the same
concentration — for instance, to one equivalent in a cubic
centimeter; or if we imagine (Ostwald) the use of elec-
trodes, which remain at a fixed distance apart of i centime-
ter, but which with increasing dilution of the electrolyte
always increase in area, so that the volume of liquid
included between the electrodes always contains just one
equivalent of the electrolyte. The conductivity of one
equivalent in its varying dilutions, thus observed, is
evidently a magnitude capable of giving information as to
the change of the molecular condition, in so far as this
influences the conductivity. Indicating the equivalent
conductivity by A, and the concentration, in equivalents
K
per c.c., by tj} then A = — .
Now Kohlrausch had found that the equivalent con-
ductivity A increased with increased dilution for all
electrolytes and in many cases approached a limit value
A 0 for very great dilution. This best attainable con-
ductivity A 0 the theory of Arrhenius conceives as belonging
to that molecular condition which consists essentially
of ions, so that it can devote itself entirely to the trans-
portation of current, while at higher concentrations the
1 Concentration in normals c = equivalent /liter stands to this in the
. c
ratio — =1000.
n
FUNDAMENTAL CONCEPTIONS OF THE THEORY. 21
values for A (< A 0 ) are characteristic of the extent to
which the molecule is ionized.
If this conception is correct, there must exist a very
simple law for the A 0 values of different electrolytes when
we consider the manner in which these are dependent on
the nature of the ions. Suppose we indicate by u the
velocity given to any cathion by the potential fall of i
volt per centimeter, by v the corresponding value for an
anion, and recall the fact that, according to Faraday’s
law, the charge of F coulombs carried by each equivalent
of any ion is always equal, then in one second there will
be moved between the electrodes mentioned above u-F
coulombs by the cathions in the positive direction, and’
simultaneously v-(—F) couloinbs by the anions in the*
negative direction, that is, the total current flowing wall,
be
A 0 =u-F— v-(— F)=u-F+v-F=(u±v) -F COU ^-
sec.
or amperes. Since u and v depend entirely on the nature
of the ions, it follows that the A 0 values of different
electrolytes must be purely additive, i.e., composed of
factors characteristic of the two ions, so that, for instance,
the differences for K and Na salts should be exactly the
same whether derived from the chlorides, nitrates, etc.,
for
(U}H-\-Va)F— (Uiz a -h‘VcdF=(Uj£ + Viio)F — (^Na + ^NO^F
= (U'K. — U Na)F.
This relationship was in fact discovered by F. Kohl-
rausch in 1876, and is called the law of the independent
22 THE THEORY OF ELECTROLYTIC DISSOCIATION .
migration of the ions. This law, which, as the formula
shows, does not directly give individual specific ionic
velocities but only the differences of two such, may be
illustrated by the following small table, which includes the
figures of those K and Na salts whose acid radicals are
given in the first column :
K ' "■
J =— for iooo n — c=o.gq£>i Eqtjiv. /Liter.
V
(Kohlrausch, 1900 and 1885 )
K
Na
(u K ~u Na )F
Cl
129 .1
108 . 1
21.0
no 3
12 5-5
104 . 6
2O.9
io 3 ..
97.6
76.7
20.9
(so 4 )^
133-5
no. 5
23.O
£(*ci -’to,)-
F *so, -*ro 3 i
F ^o 3 - v io 3 )
3 1 -5
35-9
27.6
3 1 -4
33-8
27.9
For a large class of electrolytes, namely, almost all
salts as well as the strong acids and bases, the values of
A 0 may be obtained by direct measurement, since with
increasing dilution the values of A show clearly a con-
vergence toward a limiting value, as can be seen from
the following series for KC 1 (i8°) (Kohlrausch, 1885).
Potassium Chloride (i8°).
C= I
0. 1
0.01
o.oor
0.0001
0
A — 98.2
in. 9
122.5
127.6
129.5
131.2
AA = 13.7 10.6 5.1 1.9
A similar series for acetic acid
A = 1.32 4.6 14.3 41 107
3.3 9.7 26.7 66
FUNDAMENTAL CONCEPTIONS OF THE THEORY. 23
gives no evidence of such a convergence in dilutions
experimentally accessible, as is typical of all weak electro-
lytes. In such cases, however, A 0 can be obtained in-
directly by means of Kohlrausch’s law, by making use of,
for instance in the case of acetic acid (H acet.), the ex-
perimentally accessible A 0 values for K acet., KC1, and
HC1, and calculating as follows:
^0 (K acet.) + A 0 (H C1) ~ ^0 (KC1) = ,
for
*
F[(Uk+ V ace t.) + (u s + v a) — ( M K+^a)] = -f’(^H s +^acet.);
in short,
K+acet. +H+C1— K— Cl=H+acet.
Or in words, we begin with A 0 of a salt of the weak acid
and add to it the difference between the A 0 values of a
strong acid and its salt, which has the same cathion as the
salt of the weak acid.
A prime criterion of the correctness of the course of
reasoning lies in the conclusion that the equivalent
conductivities A 0 for “ infinite dilution,” calculated with
the aid of Kohlrausch’s law, must under all circumstances
be greater than the experimentally determined equivalent
conductivities A of weak electrolytes; for if A differs
from A 0 , this can only be in the direction corresponding
to an incomplete ionization, because A 0 is necessarily
associated with complete ionization.
For concentrations in which all the molecules do not
24 THE THEORY OF ELECTROLYTIC DISSOCIATION.
split up into ions, the degree of ionization being less than
i, the equivalent conductivity will also have to be smaller
than A 0j for if there are present per equivalent only a ions,
a indicating the degree of ionization, then for each equiv-
alent only (analogous to our findings for A 0 , p. 21 ),
, , . „ coul.
A =a(u+v)F ^
can be carried. Substituting from the above equation
the value for A 0y
A
the sought-for new definition of the degree of ionization
(dissociation), determinable by electrical means. The
above consideration, that the measured A values must
always be less than the A 0 values calculated by means of
Kohlrausch’s law, is confirmed without exception by ex-
perience. We are therefore justified in building further
on this foundation and in looking upon the ratio of the
equivalent conductivity A , of a particular concentration,
to A 0 (exterpolated or calculated as above) at infinite
dilution, as the direct measure of the degree of decom-
position into ions, and in formulating, as did Arrhenius,
the equation for the degree of ionization
The dissociation theory withstood the first crucial test
in that a , the degree of ionization calculated from the
FUNDAMENTAL CONCEPTIONS OF THE THEORY. 25
equivalent conductivities, showed such surprising agree-
ment with that given by the deviations of the osmotic
-'pressure according to the formula (p. 9)
i=n-a + (1 — a) = i~r(n— 1) °l
or
i —1
a
71 — 1
(2)
The following figures, taken from freezing-point deter-
minations of Arrhenius and others, show this agreement:
Comparison of the Osmotically and Electrically Measured
Abnormality Factors.
(van’t Hoff and Reicher, 1889.)
Salt.
Concentra-
tion.
♦
(osmot.).
i
(freez.).
i
(electr.).
KCI
0. 14
1 .81
_
1.86
NH 4 C 1
00
"tf-
H
o'
I.82
—
I.89
Ca(N 0 3 ) 2
0.18
2.48
2-47
2.46
K 4 Fe(CN) 6
°- 3 S<>
3-°9
— ■
3-°7
MgSO,
O.38
1-25
1.20
i -35
LiCl
O.I3
1.92
i -94
1.84
SrClj
O. l8
2.69
2.52
2-51
MgCl*.
O. 19
2.79
2.68
2.48
CaCl 2
O. 184
2.78
2.67
2 .42
CuCLj —
0.188
—
2.56 ;
2.41
Na 6 C 12 0 12
O.OOl8
5 * 9 2
~
With this there were at hand two methods, differing
in principle yet giving like results for getting at the dis-
sociation relations of the long list of electrolytes. The
results of these investigations, carried out by Arrhenius
and the Leipzig School under the leadership of Ostwald.
may be summarized as follows:
26 THE THEORY OF ELECTROLYTIC DISSOCIATION .
1. Strong electrolytes are such salts, acids, and bases
which even in considerable concentrations ionize very
much more than half and contain as cathions any alkali
metal (Cs, Rb, K, Na, Li), or as anions one of the acid
residues N0 3 , CIO3, CIO4; furthermore, combinations
of the following cathions and anions in so far as they are
soluble:
r NCV
NH 4 -, Ba”, Sr", Ca” Mg", 1 F, Cl', Br', I'
Mn", Zn", Fe*‘, Co", Ni”, with S0 4 ", S 2 0 6 "
Pb-, H*, Hg 2 **, Ag* Cr0 4 ", Cr 2 0 7 "
CClsCOO'
Accordingly we have belonging here all alkali salts,
nitrates, chlorates, perchlorates, as well as the strong
acids HC1, HBr, HI, HNO s , H 2 S0 4 , H 2 F 2 (the last two,
it is true, are markedly less ionized than the previous ones)
also all sulphonic acids, and practically speaking all solu-
ble neutral salts, the ammonium and substituted ammonium
salts inclusive; of the bases, that is, the hydroxyl com-
pounds, we have only the tetra-substituted amine bases,
while ammonia and the substituted amines up to. the
tri-substituted belong to the next class.
2 . Weak electrolytes include first of all the three large
classes of the organic carboxylic acids, phenols, and
primary to tertiary substituted amine bases; also am-
monia, and the following compounds which form an
exception to the other neutral salts:
CdCl 2 , CdBr 2 , Cdl 2 „ HgCl 2 , Hg(CN) 2 , Fe(CNS) 3 ,
FeF 3 , Fe(acet:) 3 ,
FUNDAMENTAL CONCEPTIONS OF THE THEORY . 27
and the weak inorganic acids:
H 2 S, HCN, H3BO3, H3PO0, H3PO3, H3PO4,
H 2 C 0 3 , H 2 SO s , HoSeOs, HN 0 2 , HCIO, HIO3, HI 0 4 -
A large number of inorganic salts not included in the
above, such as those of the last-named acids, show the
phenomenon of hydrolysis and will receive special men-
tion later (p. 92).
Between these two extreme classes of electrolytes we
have, of course, all transitions, for the two classes are only
gradually differentiated, since, as has been mentioned and
as will later be discussed in detail, the degree of ioniza-
tion is greatly dependent upon the concentration. A
kind of transition class, designated as electrolytes of
medium strength, might be set up, consisting on the one
hand of the salts of the heavy metals, and on the other of
the strongest carboxylic acids, such as tartaric, citric,
oxalic, and formic, also many halogen and nitro- sub-
stituted carboxylic acids.
For reasons to be mentioned later, a very special interest
attaches to the extremely weak electrolytes, which are
transitions from electrolytes to chemical compounds
incapable of electrolytic dissociation. These will be dis-
cussed in a chapter to follow, and figures given which are
characteristic of them; here it will be sufficient to say
that they include hydrocyanic acid, hydrogen sulphide,
boric acid, carbonic acid, phenol, and above all waters
also the bases aniline, pyridine, etc. (see table, p. 53).
In addition to the conductivity method for determining
the degree of ionization we have another electrical method,
28 the theory of electrolytic dissociation.
based on the Nemst theory of concentration chains.
x\ccording to this the electromotive force of such chains,
in which the same electrode metal dips into a concentrated
and a dilute solution, is proportional to the logarithm of
the concentration ratio of the metal ions in the two
solutions. Since the mathematical form of this function
requires extremely accurate measurements in order to
determine small differences of ionic concentrations, this
method has not been applied for this purpose until recently
by Jahn (see p. 120), though it has been employed with
great success in recognizing the extremely small ionic
concentrations of very difficultly soluble electrolytes.
MOBILITY OF THE IONS.
The figures enumerated on p. 22 show that the con-
ductivity differences between alkali salts of the same
acid are independent of the nature of the acid, that
is, they are evidently dependent only on the difference of
the cathion. In a similar way we get equal differences
for a change of the acid constituents, no matter from what
alkali salts we take the conductivities. It is necessary
to take only one step further in order to determine, in the
case of any salt, how the conductivity is divided between
the anion and cathion, and to calculate from the above
table the part each ion takes in the conductivity. This
was done in the classical researches of Hittorf on the
concentration changes in the vicinity of the electrode
during the electrolysis of salts, and permits drawing a
conclusion as to the apportionment for the two ions in
transporting the current.
Suppose we conduct a definite amount of electricity,
say 96580 coulombs, the quantity carried by one ion
equivalent, through an electrolytic cell, then
1. At each of the electrodes, according to Faraday’s
law, one equivalent of the respective ions is separated.
This we shall look upon either as remaining in solution,
as is actually the case in the electrolysis of salts such
as KgSO^ or ? in case it is precipitated, as belonging
30 THE THEORY OF ELECTROLYTIC DISSOCIATION .
to the solution immediately surrounding the particular
electrode.
2. It is necessary for us to gain some insight into the
mechanism of the current transport in so far as it takes
place within the solution, i.e., between the electrodes.
Of our 96580 coulombs one part is carried by the positive
ions and the other part by the negative ions in their
wandering to the electrodes, so that a certain quantity of
anions move away from the cathode and a certain quantity
of cathions away from the anode and will be wanting at
their former places. It can readily be seen that this
reduction of the concentration at the electrodes must give
a measure of the nature of the ratio of the rates of migra-
tion of the ions wandering in opposite directions. For
example, in the case of equal mobility, that is, like rates
of wandering for cathions and anions, the reduction in
concentration of these ions at the electrodes from which
they migrate must be exactly equal; with unequal mobility
the reduction in concentration must be greater at the
electrode from which the ion of greater velocity moves.
The ratio of these ionic concentration reductions at both
electrodes, as measured by Hittorf, represents, in other
u
words, the ratio in which the transport of current dis-
tributes itself between both ions. Calculating from the
shifting of the concentration of one of the ions the cou-
lombs carried by the ionic matter transported away, and
comparing this with the total coulombs (measured, for
example, by means of a voltameter) which flowed through
the electrolyte during the time in which the measured
concentration change took place, we obtain the so-called
MOBILITY OF THE IONS.
3 1
transference number, which represents the fraction
u j v \
— ; — ( or — ; — I of the total number of coulombs trans-
u+v \ u+vj
ported by this ion. The transference number i for
the cathion of a given salt would mean that the entire
transportation of current was carried on by the cathion,
while the anion had no part in it whatsoever. This,
however, could take place only in the extreme and non-
existent case of the mobility of the anion being infinitely
smaller than that of the cathion, for, as both ions are
moved by the same electrical driving force, their velocity
must be proportional to their mobility. The transference
number 0.5, which, on the other hand, is not infrequently
found at least approximately, would indicate that the
electric current is carried half by the cathion and half
by the anion, or that both ions possess the same mobility.
The most exact measurements of transference numbers
made are those with potassium chloride, which give for
the ion K the value 0.497.
Now we know' from Kohlrausch’s measurements that
for KC 1 (see p. 22)
A 0 = (u -f ^96580 = 1 30.1 ,
and with the aid of the second equation,
u
u+v
0.497,
we are in position to calculate separately the values for
u and v. In order to avoid too small values, it is better
to employ, instead of the “ absolute mobilities ” u and v,
32 THE THEORY OF ELECTROLYTIC DISSOCIATION.
the “ electrolytic mobilities ” Ik and l A for cathion and
anion, which are 96580 times greater. We may then
write
A 0 =l K +l A = 96580(11 +v)=i 30.1
and
U
U + V Ik+Ia
from which we get for the potassium ion
l K = 64.67,
and for the chlorine ion
/ A = 65.44.
These values at once enable us to get at the mobility
of other ions by using the equivalent conductivities of
other potassium salts and other chlorides, and subtracting
from these the mobility values of K* and Cl' respectively.
What is more, we are also in position to calculate the
maximum equivalent conductivity for such electrolytes
whose measurements do not show any such maximum
conductivity.
For example, in order to obtain the electrolytic mobility
of any anion, say F', it is only necessary- to know A 0 for
KF, which Kohlrausch (1902) found to be
Subtracting from this Ik = 64.67
we have left / FW ne= 46.68
MOBILITY OF THE IONS.
33
The mean values of the most accurately known elec-
trolytic mobilities 1 at i8° are given (according to Kohl-
rausch 2 3 ) along with their temperature coefficients a in
the following tables:
1 The l values give the conductivity of i mole of the ion in i c.c. (not
in i /!).
2 Berl. Akad. Ber., 26 , 586 (1902).
3 For the H* and OH' ions the electric mobilities are known with a
much less degree of certainty, since it is impossible to follow up the A
values of acids and bases to the very great dilutions where the con-
ductivity of the water and its unavoidable impurities play a part not
yet determined.
34 THE THEORY OF ELECTROLYTIC DISSOCIATION.
These numbers enable us to calculate by addition A 0 ,
the equivalent conductivity at infinite dilution, for all
salts formed by combinations of the above ions. They
have been amply confirmed by the fact that the trans-
l
ference numbers ; — — calculated from these values
agree admirably with those found.
Evidently an exceptional position is held by the ions
of water, H* and OH', of which the former is about five
times and the latter about three times as mobile as the
most mobile of its kind. In consequence of this, among
the strong electrolytes the acids and bases (comparing
equivalent solutions) are much better conductors than
all neutral salts.
For electrolytes with ions of greater valence the relations
are more complex, in that the values for A do not converge
sufficiently at convenient dilutions to give accurate values
for Aq. However, as has recently been shown by Steele
and Denison , 1 in the case of such electrolytes the trans-
ference numbers, which vary considerably with the con-
centration, converge toward values showing a good
agreement with the A 0 values measured by Kohlrausch.
A regularity in the magnitude of the mobilities may be
formulated for organic anions in the statement that the
mobility decreases at first rapidly and then more slowly
with increase in molecular weight. For the inorganic
ions, however, this rule does not hold; it seems, on the
contrary, that some other influence, as in the group of the
alkali and alkali- earth cathions, plays a part here which
1 journ. Chem, Soc. Trans., 81 , 466 (1902).
MOBILITY OF THE IONS .
35
probably must be sought for in hydration. It is
notable that the halogens as ions, in spite of their varying
weight and varying mobility in the form of diffusing
neutral molecules, possess almost equal mobility. Euler 1
offers as an explanation for this the assumption of marked
hydration, which might equalize the difference in weight.
Possibly this hypothesis finds support in the observation,
that in the series of the alkalis, as well as the earths,, the
element of strongest electro-affinity (compare p. 159),
which may be assumed to have the least tendency to
hydration, forms the most mobile ion.
A very comprehensive research and summarization of
the mobilities of all known inorganic as well as organic
ions and the accompanying regularities, we owe to
Bredig. 2 He found among other things that the mobility
of the* element ions is a periodic function of the atomic
weight; that for compound ions it essentially holds that,
increasing the number of atoms decreases the mobility;-
and that constitutional influences also make themselves,
felt.
The slowest known anion is that of the lactone of
^-toluido-/ 9 -i-butyric acid with l a (2 5°) = 23.3; the slowest
cathion, that of aconitine with Ik (2 5 0 ) = 17.8.
The influence of temperature on ionic mobility has
recently been more carefully investigated by Kohlrausch, 3
with the result that to each ion an independent change
of mobility can be attributed, as was to be expected in
accordance with the additive law (p. 12).
1 Wied. Ann., 64 , 273 (1897).
2 Zeitschr. physik. Chem., 13 , 191 (1894).
5 Berl. Akad. Ber., 26 , 574 (1902).
36 THE THEORY OF ELECTROLYTIC DISSOCIATION
These individual temperature coefficients are to be
found under a in the above table of mobilities. They
mean that the values for l are to be multiplied by
(1 4- [t— i8]a) in order to obtain the values for l at ^°. It
is of importance to note that these percentage temperature
coefficients are smaller the larger the mobilities; the
absolute coefficients, however, show the same order in
the series as the mobilities, so that the ions converge in
the direction of lower temperatures toward the same
mobility.
From the changes in mobility of the ions we can now
also calculate the influence of temperature on the con-
ductivity for other concentrations than that of extreme
dilution, in so far as we are allowed to assume that
essentially the ionic mobility changes and not the degree
of dissociation, i.e., the number of ions that take part in
the conductivity at the different temperatures. According
to the results of investigations on this point, to be dis-
cussed later (see pp. 135, 140), this assumption holds
approximately for strong electrolytes and also for many
weak ones whose heat of dissociation is small, so that
their temperature coefficients can be calculated from the
above values. The percentage coefficients for salts lie
between 0.021 and 0.029, for acids in the neighborhood
of 0.013, f° r bases near 0.020.
EQUILIBRIA AMONG IONS.
Starting with the conception that dissociation is to be
considered as a chemical reaction of such a nature that
out of the ions, the dissociation products, the undissociated
substance is formed by chemical interaction, then we
must look upon the law of mass action as the factor
determining the equilibrium between the reacting ions
and their resulting undissociated product. During the early
days of the dissociation theory it was customary to view
this reaction from the side of the undissociated molecule,
the ions being formed by its decomposition. In principle,
however, both mean the same, and it is clearer possibly
from a chemical standpoint to consider the reaction in
the reverse sense as we did above, and to look upon the
ions as primary and their product, the undissociated
compound, as secondary. Indeed, the latter seems more
natural — though fundamentally a matter of taste — in
so far as the presence of ions is an extremely wide-spread
property of chemical substances. Yet not incorrectly
perhaps and from purely historical reasons, one considers
the inappreciably ionized compounds belonging essentially
to organic chemistry as the normal, owing to their great
number and the intensity of the study that has been con-
centrated upon them.
THE THEORY OF ELECTROLYTIC DISSOCIATION.
If, however, we take as the normal the relations as they
prevail with the compounds which show the greatest
variation in the elements combining to form them, that
is, without favoring carbon compounds, then ionic dis-
sociation is of such- a general nature that we may place
ionic interaction or the formation of undissociated com-
pounds in the foreground.
It is true, science proceeded in just the opposite way:
the undissociated compounds were considered the normal
ones. The formation of ions was formerly unknown and
in a certain sense did not take place until the introduction
of the theory, because not until then was it a conscious
change. But however that may be, the compounds which
are very little ionized represent such whose components
are held together by. exceptionally strong forces of atomic
affinity, while the chemical relationship between the
components (ions) of the strongly dissociated substances
must be considerably less, in order to make possible for
them the independent existence.
A thing difficult of conception also lies in the assumption
that a reaction is to arise out of an undissociated substance
without that substance interacting with other substances;
this in fact becomes inconceivable when one assumes the
hypothesis, to be discussed later, that all reactions are
dependent on the presence of ions, and that , their velocity
is directly determined by the concentration of the ions
necessary for the reaction. Suppose we picture to our-
selves a molecule, capable of ionization, in an entirely
undissociated state, then a dissociation into ions cannot
take place at all, because according to our assumption
the undissociated substance was to have no ions. We
EQUILIBRIA AMONG IONS.
39
can readily conceive of the reverse, for when ions are
once present, undissociated substances form by their
reaction. For this it would be necessary, of course, to
assume that no chemical element could exist in the state
of an absolutely electricity-free non-ion. However, we
shall not here continue these speculations, for they are
of no consequence as far as the numerical laws of dis-
sociation are concerned.
For the dissociation of substances such as ammonium
chloride, phosphorus pentachloride, and others, which in
the gaseous state split up into simpler components, the law
of mass action has shown that the product of the con-
centrations (partial pressures) of the reacting constituents
is proportional to the product of the concentration of the
substances produced by the reaction. Now precisely
the same mathematical relation must also hold for dis-
sociation into ions and the reaction of ions to form un-
dissociated molecules. And it was the great service of
Ostwald to have recognized this law and confirmed it for
a much wider range than that for which it had been estab-
lished for the then known gas dissociations. This law reg-
ulates the concentration of the ions and undissociated
molecules with varying total concentration of the solution.
In other words, it places us in position to derive from the
degree of dissociation of an electrolyte at one concentration
the degree of dissociation at any other desired concentra-
tion. If, for instance, for the concentration c, the degree
of dissociation, or the part per mole split up, is a , then the
total concentration of each ion is a -c, and the concentra-
tion of the undissociated remainder is (i —a) c. Intro-
ducing this value into the law of mass action, we get for
40 THE THEORY OF ELECTROLYTIC DISSOCIATION.
the product of the concentrations of the reacting sub-
stances (the ions), for the simplest case of a binary
electrolyte in which two ions unite to form an undissociated
molecule,
(a • c) • (a - c).
This product is to be proportional to the concentration
of the undissociated substance, namely (i — a) Hence
for a binary electrolyte the expression for the law of
mass action is
a 2 'C 2 =^k -( i —a) c,
if k indicates the proportionality constant which is
characteristic (at a definite temperature) for this reaction.
Now having found the degree of dissociation a for the
concentration c, by means of one of the above methods,
i.e., conductivity or osmotic pressure measurements
(freezing-point, boiling-point, etc.), we can calculate
by the given formula the “ dissociation constant ” k and
are then in position to determine the degree of dissociation
for other concentrations (c values) with the aid of the
transformed equation
a 2 k
i —a c
\ 3 )
or
— £+\/£ 2 +4 kc
a = .
2C
EQUILIBRIA AMONG IONS. 4 *
or neglecting k 2 and k as compared with \ which is
permissible for small values of k, we have approximately
Ik
a = y!- ( 3 a )
The testing of this important relation, the so-called
dilution law of electrolytes discovered by Ostwald , 1 was
first undertaken by van’t Hoff and Reicher 2 on a series
of acids and resulted in an excellent confirmation. The
authors close their discussion with these words: “Not
a single case of ordinary dissociation has been tested
within such wide limits.” Some of the figures are given
in the following tables:
Acetic Acid: £ = i.78X io ~ 5 (14 0 ).
_ J
c
0-994
2-02
15-9
1S.1
1500
3010 74S0
15000
100 a from conductivity A . .
0.40
0.6l
1.66
1.78
14-7
20.530.I
4O.8
100a from k calculated
p.42
0.60
1.67
1.78
15 -°
20.2 3O.5
40.1
Monochloracetic Acid: k = i .$ 8 Xio - 3 (14 0 ).
_ X __
c
20
205 40S
2060 4080
IOIOO
20700
100 a from A found
16.6
42.3 54-7
80.6 88.1
94.8
96.3
1 00a from k calculated. . . .
16.3
43 -° 54-3
80.1 S8.0
94-4
97.1
Ostwald about the same time, in amassing his extended
observations on the organic carboxylic acids, used a
1 Zeitschr. physik. Chem., 2 , 36 (1S8S).
2 Ibid., 2 , 777 (18SS).
42 THE THEORY OF ELECTROLYTIC DISSOCIATION.
method, which since then has remained the customary
one, so that usually the law of mass action is tested not by
comparing observed and calculated degrees of dissociation,
but by testing whether the expression for the characteristic
dissociation constant.
gives values independent of the dilution. Since in the
majority of cases a , the degree of dissociation, is obtained
with the aid of conductivity, i.e., from it is practical to
insert this expression directly into the formula, giving it
the form
or
A 2 -c
A 0 (Ao-A)
= k,
( 4 )
or finally, introducing the specific conductivity k=A-c:
* _*
A g (A 0 -c-k)
For the relatively frequent case of very weakly dis-
sociated electrolytes, in w T hich the degree of dissociation
a is only a small fraction (say 1% or less) of the total
concentration, the general formula can be conveniently
EQUILIBRIA AMONG IONS .
43
simplified by writing i — a = i, by reason of the smallness
of a , when it becomes
a 2 -c = k or
A 2 c
A 0 2
( 5 )
From the latter equation a very simple law for the
variation of conductivity may be derived. Since J 0 for
one and the same electrolyte is constant, being independent
r , . , . Const,
of the concentration, we have simply = — - — or A
inversely proportional to Vc. Finally, the equivalent
conductivity being A = wherein k is the specific con-
ductivity, we can, by substituting in the last equation,
so formulate the relation between the specific conductivity
k and the concentration of the electrolyte that
a : 2 — Const . - c or jc = Const . * V 7 c,
which means, in other words, that the conductivity of a
solution with varying concentration is proportional to
the root of this concentration. For example, diluting a
solution four times reduces the conductivity only one
half, or diluting ten times reduces it only 3.16 times.
This is shown by the following small table for acetic
acid, taken from measurements of Kohlrausch:
. Acetic Acid (iS°).
C— 1.0
O 5
0.1
0.05
0.0 1
0.005
0.00 1
0.0005
0.0001
K = I* 3 2
.4=1.32
1.005
2 0 :
0.46
,1 . 60
0.324
6. 4 3
0.143
14 - 3 .
0. 100
20.0
0.041
41.0
0.0285
57 -o
6.0107
107.0
44 THE THEORY OF ELECTROLYTIC DISSOCIATION.
The following tabulated figures are taken from the
previously mentioned measurements of Ostwald, given
for the greater part in Zeitschr. physik. Chem., 3 , 170,
241, 369 (1889), as well as from those of Bredig. 1 Here
IQ ° : - expresses the degree of dissociation in percentages.
- 1 0
I
Acetic Acid :
4 o =3 SS
Monochloracetic Acid :
Aq — 386
Dichloracetic Acid:
A 0 = 3S5
v— —
c
A
iood
- 4 o
io 5 fe
A
TOO A
Ao
io 5 k
A
.
100 4
^0
io 5 &
16
6 -5
1-67
i- 79
56.6
14.6
J 55
269.8
—
—
32
9.2
2.38
1.S2
77.2
19.9
I 55
70. 2
5170
64
12.9
3-33
1.79
IO3.2
26.7
152
309-9
80.5
520°
I2S
18. 1
4.6S
i -79
136. 1
35 - 2
150
338-4
‘88.0
5040
256
25-4
6.56
1 .So
174.8
45.2
146
359-2
93-4
5 i6 °
5 12
34-3
9.14
1.80
219.4
q6.S
146
375-4
97.6
—
1024
49-0
12.66
i -77
265.7
6S.7
147
383-8
99-7
Ammonia: Aq=^ 253
Methylamine. J 0 = 240
Piperidine: A 0
= 216
T
v= —
c
A
ioo 4
Aq
io 5 k
A
100A
4 )
io 5 k
A
100A
Ao
IQSJfe
8
3-4
i -35
2 -3
I 5 - 1
6 -3
52
23.O
10.6
157
16
4.8
1.88
2 -3
21.0
8.7
5 2
3 2 '3
14.9
163
3 2
6.7
2.65
2 -3
28.9
12.0
5 i
44.2
20.3
162
64
9-5
3- 76
2 -3
39-3
16.3
50
59-2
27.2
159
128
13-5
5-33
2 -3
53 -o
22.0
49
77.8
35-8
156
256
18.2
7-54
2.4
70.0
29.I
47
99-7
45-9
152
That the measurements of the degree of dissociation
from determinations of the freezing-points lead to the
same results is shown by the following series of observa-
1 Zeitschr. physik, Chem., 13 ? 289 (1894),
EQUILIBRIA AMONG IONS .
45
tions: A indicates the depression of the freezing-point,
1.85 the depression in water of each mole of undissociated
substance.
Tartaric Acid.
(Abegg, 1896.)
c
1
c
I - S A
a—i — 1 !
H
a
C
0.00516
2.45°
I.32
0-32 ;
°- 35
0.0103
2.29
1.24
0
to
4—
0.26
0.0154
2 . 24
1. 21
0.21
0. 22
0 . 0204
2.23
I.205
0.205
0. 20
0.0254
| 2.18
I. IS
0 . iS
0. iS
0 . 0303
2.15
I .16
0. 16
0. 16
°-°353
1
2 -OS
1. 12 j
0.12
0.15
The extent of the observations confirming the dilution
law — in other words, showing the validity of the law of
mass action — -may be seen by a glance at the comprehensive
tables to be found very systematically arranged in the
excellent book of Kohlrausch and Holbom, 1 “ Leitver-
mogen der Elektrolvte,” pp. 176 to 194.
Of this material the greater part relates to weak organic
acids and is taken from the researches of Ostwald and
his pupils, 2 among whom Walden is to be especially
mentioned. A smaller part consists of the measurements
of Bredig 3 on bases, among which especially the weak
amine bases confirm the dilution law.
1 Teubner, .Leipzig, 1898.
3 The complete literature is to be found in the mentioned work of
Kohlrausch and Hqlborn.
* Zeitschr. physik. Chem., 13, 2S9 ( 1894 ).
THE DISSOCIATION CONSTANT.
This great mass of material naturally offered not only
a confirmation of the mathematical formulation of the
relation between the degree of dissociation and the
concentration of the electrolyte, but also enabled us to
gain important chemical knowledge from the measure
of the dissociation constant. This constant is indeed an
expression of the chemical nature of substances, in that
it gives a numerical measure of the tendency to split into
ions. If we do not apply the above form of the dissocia-
tion constant given by Ostwald, but rather its reciprocal
value p then this would constitute an analogous numerical
expression for what we have previously termed the atomic
affinity, which exists between ions and tends to produce
undissociated molecules out of them.
The physical significance of the constant k can also be ex-
pressed, with Ostwald, as indicating one half of that concen-
tration at which the various electrolytes possess exactly the
degree of dissociation equal to J. For example, taking
for comparison the constant of acetic acid (0.000018),
of monochloracetic acid (0.00155), °f dichloracetic acid
(0.051), and also let us say of malonic acid (0.00158)
and maleic acid (o.oi2) ? it means that these acids are
46
THE DISSOCIATION CONSTANT.
47
dissociated 50% in solutions which for acetic acid have
the normal concentration 0.000036, for monochloracetic
acid 0.0031* for dichloracetic acid 0.12, for malonic
acid 0.00316, and for maleic acid 0.024. The definition
for \/ k taken from the formula (3 a), p. 41, is pos-
sibly clearer, \/k being the ionic concentration present
in the i-normal solution of the electrolyte. Since the
action of acids is determined by the concentration of
the hydrogen ion, that of bases by the hydroxyl ion, it is
easy to see the great value of knowing this dissociation
constant in comparing chemical nature, and it was to be
expected from the very first that this characteristic
constant should bear a marked relationship to the chemical
constitution of these substances. This has in fact been
found to be true, and as it is our desire to trace at least
the bolder outlines of this relationship between chemical
nature and the dissociation constant, we shall bring
together in 'the following tables the dissociation constants
of some interesting acids.
Substitution or CH 3 .
Formic add, HCOOH £=127.0 Xio— 5
Acetic acid, CH 3 COOH 1.8 Xio -5
Propionic add, CoH 5 COOH 1.3 Xio~ 5
Butyric acid, CaHyCOOH 1.5 Xio~ 5
Isobutyric add 1.45X10- 5
Valeric add, QH^COOH 1.6 Xio~ 5
Caproic add, C5H11COOH. 1.45X10 -5
While the first substitutions without doubt produce a
weakening of the acid, the very first as much as seventy
times, the subsequent ones are occasionally accompanied
by . a slight strengthening.
48 THE THEORY OF ELECTROLYTIC DISSOCIATION.
Substitution of Halogens.
Acetic acid
Chloracetic acid
Dichloracetic acid
Trichloracetic acid
Bromacetic acid
Cyanacetic acid. . .
Sulpho-cyanacetic acid
*55
5 100
138
— 370
Lactic acid
Trichlorlactic acid
Propionic acid
/?-Iodpropionic acid
9.0X10- 5
Benzoic acid
w-FIuorbenzoIc acid
Here one sees that all these substitutions bring about
a very marked strengthening, and again that with several
successive ones — as in general — the first step is the most
effective; furthermore, that the proximity of the substitut-
ing groups is of great influence, as will later be pointed
out more fully.
Substitution of OH.
Acetic acid, CH 3 COOH io 5 X k= i . 8 .
Glycollic acid, CHjOHCOOH 15.0
Propionic acid, CH 3 CH 2 COOH 1.3
Lactic acid, CHjCHtOHJCOOH . 14.0
^-Oxypropionic acid, CH^OH) CH 2 COOH . 3.1
Benzoic acid, C 6 H 5 COOH 6.0
Salicylic acid, C 6 H 4 (OH)COOH (1:2).... 102.0
•w-Oxybenzoic acid, C 6 H 4 (OH)COOH (1:3) 8.7
^-Oxybenzoic acid, C e H 4 (OH) COOH (1:4) 2.9
THE DISSOCIATION CONSTANT .
49
The nearer to the COOH group the OH is introduced,
the more it increases the dissociation of acids; the same
is true of N 0 2 and COOH:
Substitution of NO*.
Benzoic acid io 5 X&= 6.0
<?-Nitrobenzoic acid 620 . o
w-JNTitrobenzoic acid 35 .0
^-Nitrobenzoic acid 40.0
Phenol £=1.3 Xio~ 10
n-Nitrophenol 4.2 Xio~ s
2,6-Dinitrophenol 1.7 Xio" 4
Trinitrophenol 1.64X10— 1 t 1 )
Salicylic acid io 3 X£ = 1.02
n-Nitrosalicylic acid 115 .7
^-Nitrosalicylic acid 9.0
Substitution of COOH.
Acetic acid, CH 3 COOH 10 s X k = 1 . 8
Malonic acid, COOHCH 2 COOH 158. o
Propionic acid, C 2 H 5 COOH : . 1.3
Succinic acid, COOHC 2 H 4 COOH 6.6
Benzoic acid, C e H 5 COOH 6.0
0-PhthaIic acid, COOHC 6 H 4 COOH 121 . o
w-Phtfcalic acid, COOHC e H 4 COOH. ... 29.0
Substitution of NH 2
exceptionally weakens the acid character, so that on the
one hand the very strong sulpho-acids, whose constants,
for reasons to be given later (see p. 121), lie beyond those
capable of measurement, are brought by substitution
within the scope of those measurable, while on the other
hand the acids of the average strength of the above are
decidedly weakened. A constant for these is not to be
■ 1 Rothmund and Drucker, Zeitscbr. physik. Chem., 46, 827 (1903),
5o THE THEORY OF ELECTROLYTIC DISSOCIATION.
obtained directly by conductivity measurements, on ac-
count of their capacity for amphoteric (acid and basic)
dissociation; however, B redig and Winkelblech 1 showed
how both the acid and basic dissociation constants may
be obtained (see table, p. 55).
Influence of the Position of the Substituting Groups.
In addition to the preceding characteristic examples,
the series of dicarboxylic acids may be given:
Oxalic acid, COOH.COOH
Malonic acid, COOH.CH 2 .COOH. .
Succinic acid, COOH.C 2 H 4 .COOH. .
Glutaric acid, COOH.C 3 H G .COOH . .
Adipic acid, COOH.C 4 H S .COOH . . .
Pimelic acid, COOH.C 5 H l0 .COOH . .
Suberic acid, COOH.C 6 H 12 .COOH . .
Sebacic acid, COOH.C s H 1G -COOH..
io 5 Xj&= about 10000
158
6.65
4-75
3-7
3-6
2.6
2 -3
Methylmalonic acid,
COOH.CH(CH 3 ).COOH
Pyrotartaric acid,
COOH-QHaCCEy. CO OH
„ . COOH.CH
Fumanc acid, r 3v .
CH.COOH... io 3 X&=
, CH.COOH
Male* aad, g H-COO jj
87
8.6
o-93
11.70
In these instances the essential relation coming into
play is the distance apart of the two COOH groups:
the more carbon atoms between them the weaker the acid
becomes — here again the first steps are decidedly the most
effective. Upon attaining a certain separation a further
increase of the distance makes less and less impression.
1 Zeitschr. physik, Chem., 36 , 546 (1901).
THE DISSOCIATION CONSTANT.
5 *
Comparing fumaric and maleic acids, the action of the
proximity of the two carboxyl groups is especially apparent.
In the case of organic compounds one condition for the
production of H' ions is evidently the direct union of H
and O; for that reason the alcohols show a distinct,
even if extremely slight, acid function (the alcoholates).
Another important condition is the proximity of carbonyl
groups, which, for example, in the case of malonic-acid
ester, acetic-acid ester, and also in acetylacetone makes
the hydrogens in the neighborhood of the CH 2 groups
capable of dissociation and salt formation. 1 The carboxyl
compounds undoubtedly owe their marked acid property
to the combination of both conditions. In the repre-
sentatives of the first two groups of compounds the
dissociation is scarcely detectable by physical means;
therefore the decomposition of their salts by water (see
Hydrolysis, p. 76) is almost complete.
In the case of bases, all substituting groups have just
the reverse action of that on acids; the halogens, the
carboxyl group, and the N 0 2 group have an especially
weakening effect on the basic character. A detailed in-
vestigation of Bredig 2 gives a fuller account of this.
Because of the great influence of constitution a quan-
titative determination of the eff ect of substitution has up
to the present not been possible.
Another phenomenon deserves special mention, which
was likewise first noted and made clear by Ostwald,
nam ely, the dissociation of the dibasic organic acids.
As these contain two CO OH groups, there is a possibility
1 Ehrenfeld, Zeitschr. f. Elektrochem., 9 , 335 (1903).
2 Zeitschr. physik. Chem., 13 , 289 (1894).
52 THE THEORY OF ELECTROLYTIC DISSOCIATION.
of a hydrogen ion dissociation taking place at both of
these, the more so as we have just seen that the presence
of a second carboxyl group in the molecule markedly
increases the dissociating tendency of the first. Now,
strange to say, a calculation of the constant by equation
(3), — — which holds only for binary electrolytes
(those splitting into two ions), shows that this is not the
case. For if both carboxyl groups split off H* ions, such
an acid would have ternary dissociation, that is, would
have to obey another dissociation formula. One is forced,
therefore, to the view that the dissociation at the second
carboxyl group takes place with considerably greater diffi-
culty than at the first, so that an influence of such a nature
must be present that the first step of the dissociation
prevents the second from taking place. That a second
stage sets in at all, can be recognized by the fact that in
general the binary dissociation formula ceases to apply
when the degree of dissociation of the first stage has
reached about J, for here the constancy of the expression
cx?-c
- — — ceases (compare table on opposite page). The
physical significance of this phenomenon Ostwald finds
in that the presence of a negative charge on a univalent
acid anion makes more difficult the placing upon it of a
second ionic charge, for the electrostatic reason that like
charges repel one another. This second ionic charge
would be necessitated by a dissociation at the second
carboxyl group. One consequence of this view may be
empirically tested: the appearance of the second stage of
dissociation would have to be influenced by the relative
Second Dissociation of Dibasic Acids.
(Ostwald, 1889.)
THE DISSOCIATION CONSTANT.
Fumaric acid, COOH.C 2 H 2 COOIL
54 the theory of electrolytic dissociation .
position of the two carboxyl groups in the molecule, for
it is evident that the electrostatic interaction must be
greater the nearer the negatively charged carboxyls
are to each other. This surmise is fully confirmed. In
dibasic acids whose constitution shows a close proximity
of the two carboxyls, the second dissociation sets in
with considerably greater difficulty than in acids where
the carboxyls are farther apart. In the enumeration on
p. 53 are given the constants k of different dibasic
acids calculated according to the dilution law for binary
dissociation. At the dilution marked f the binary
constants increase, showing the beginning of the second,
the ternary stage of dissociation. Under a the two
degrees of dissociation are given, between which the
ternary dissociation begins. The most marked evidence
of the influence of the proximity of the carboxyls is given
by fumaric and maleic acids and the phthalic acids with
the adjacent position of the two CO OH groups.
As is to be seen, w-hen the two COOH groups are near
together, in spite of far-reaching primary dissociation, the
secondary does not set in until very late (a-nitrophthalic
acid) or not at all (maleic acid), while in most cases it
begins with a equal to about 0.5.
Of especial interest are the extremely weak electrolytes,
previously mentioned, a list of which is appended here 1
(for 25°) :
1 From Walker and Cormack, Journ. Chem. Soc., 77 , 5 (1900); Zeit-
schr. physik. Chem., 22 , 137 (1900). — Walker, ibid., 4 , 332 (1889), and
32 , 137 (1900). — B redig, ibid., 13 , 322 (1894). — Winkelblech, ibid., 36 ,
587 (1901). — Lowenherz, ibid., 25 , 385 (1898). — Morse, ibid., 41 , 709
(1902). — Bader, ibid., 6, 289 (1890). — Walker and Wood, Proc. Chem.
Soc., 19 , 67 (1903).
THE DISSOCIATION
CONSTANT .
55
Extremely Weak Electrolytes.
Acids:
Meta-arsenious acid, H*, AsO/
. 2.1 Xio~ s
w-Amidobenzoic acid, H',
C 6 H 4 (NH>)COO'
9.6 X io~ 6
Carbonic acid, H*, HCO s '
3.04X IO“ 7
^-Nitrophenol, H*, C G H 4 (NO.AO'
1.2 X io~ 7
Hydrogen sulphide, H*, SH'
5.7 Xio~ s
Boric add, H*, H^BO/-
1.7 Xio-®
Hydrocyanic acid, H', CN'
1.3 Xio- 9
Alanine, H-, CJS 5 (NEQCOO'
9.0 Xio -10
Phenol, H*, C 6 H s O'
1.3 Xio- 10
Water (25 0 ), H*, OH'
. 1 . 2 X io~ 14 (ionic product)
Cacodylic acid, H', (CH 3 )^AsOO'
. 4.2 Xio- 7
Bases:
^-Cumidine, OH', C^CH^H, . . .
1.7 Xio- 9
^-Toluidine, OH', C-H-NH-f
1.6 Xio- 9
Aniline, OH', C G H 5 NH 3 *
4.9 Xio- 10
w-Amidobenzoic add, OH',
C 6 H 4 (COOH)NH 3 *
1.9 X io~ u
m-Nitxaniline, OH', C 0 H,(NO 2 )NH 3 - . .
4.0 X io“ 12
Alanine, OH', CJH 5 (COOH)NH 3 '
3.8 Xio- 13
Tbiazole, OH', CftSNH*
3.3 Xio- 12
GlycocoU, OH', CH.(COJEI)NH 3
2.9 Xio -12
Asparagine. OH',
C 2 H 3 (C 0 2 H)(C 0 NH 2 )NH 3 '
1.3 Xio- 13
^-Nitraniline, OH', C 6 H 4 (NO)oNH 3 -. . .
1.0 Xio -12
Thiohydantoin, OH', C 3 H 5 N 2 SO*
9.5 Xio- 13
Aspartic acid, OH', CoH 3 (C 0 2 H) 2 NH 3 '
8.7 Xio^ 13
Betaine, OH', CH^CO^NCCH,)^. . .
7.6 Xio— 13
Acetoxime, OH', (CH 3 ) 2 CNHOH* . 6. iX 10— 13 (25°); 1.8 Xio -
13 (40°)
Urea, OH', CONJEJ,.* 1.5X10- 14 (25 0 ); 3.7X10-
14 (40°)
o-Nitraniline, OH', C 6 H 4 (N0 2 )NH3’ . . . .
1.0 Xio -14
Water (25°), OH', H’
1.2 X io- 14 (ionic product)
Acetamide, OH', CH 3 CONH 3 *
3.oXicr- 15 (25°);
3.3X10-
14 (40°)
Propionitrile, OH', CJH 5 CNH‘
1.8 Xio- 15
Thio-urea, OH', CSN*H s *
1.1 Xio- 15
Cacodylic add, OH', (GHQsAsO' . 2.5X
IO— 13 (23°); 3.8X10
- 13 (o°)
Salts:
Mercuric chloride, HgCL,
i X IO- 14
Mercuric bromide, HgBr 2
2 Xio- 18
Mercuric iodide, Hgl 2
iXio-«
the theory op electrolytic dissociation .
Among these, the dissociation of pure water into H*
and OH 7 ions is of particular importance. This constant
at room temperature is equal to about io~ 14 , i.e., the
product of the hydrogen and hydroxyl ion concentrations
has the above value, or in pure water each kind of ion is
present in the concentration io -7 . In other words, pure
water is one ten-millionth normal with reference to the
hydrogen and hydroxyl ions . 1
This value has been arrived at in four entirely inde-
pendent ways, and the different results show excellent agree-
ment. Kohlrausch and Heydweiller 2 3 determined the con-
ductivity of water purified with extreme care, after they
had discovered that the conductivity of the common dis-
tilled water is for the most part due to such substances as
carbonic acid, ammonium salts, glass, etc., dissolved from
the atmosphere and the walls of the vessel. By repeated
distillation in vacuo in specially prepared vessels of most
sparingly soluble glass, they succeeded in obtaining a
conductivity,
k=o.04Xio"~ 6 (i8°),
which in conjunction with the mobility of the H* and OH'
ions gives the named ionic concentration; since i mole
1 The constant io~ 14 is in the true sense not a dissociation constant,
but merely represents the ionic product, that is, (IT) - (OH') or k- 1 H 2 0 ) ;
since, however, on the one hand the concentration of the BL 2 0 molecules
in water is unknown (on account of polymerization), and on the other
hand practically does not vary to any extent in dilute solutions, it is
to no purpose to introduce for the ionic equilibria in which water takes
part any other constant than the ionic product, namely, k ■ (H 2 Q), which
in the future shall be designated by k or the ‘‘water constant.”
3 Wied. Ann., 53 , 209; Zeitschr. physik. Chem., 14 , 317 (1S94).
THE DISSOCIATION CONSTANT.
57
H-+OH' ions in i c.c. would produce (see p. 33) the
conductivity 318 + 174 = 492, therefore there are only
o.o4Xio“ 6 , ,
mole 10ns m 1 c.c. = o.8Xio _/ mole per
492
liter.
Ostwald followed a second method requiring much
less precision. He measured the electromotive force of
two hydrogen electrodes opposed to each other, the one
dipping into an acid, the other into an alkali, of known
H“ and OH' concentration respectively. This galvanic
combination can be looked upon as a concentration chain
of hydrogen ions, whose force, according to Nemst’s
theory, serves to determine the H' ion concentration in
the hydroxide solution employed, and in consequence
permits the calculation of the product of H* and OH' ion
concentrations. This product represents the dissociation
constant of water. The result was the same as above.
(We shall learn later how in such cases as this, where the
concentration of the two ions is very different, the law
of mass action is applied.)
A third way, that led to the same result, was the meas-
urement of the rate of saponification of esters by water,
as carried out by Wijs according to a theory of van’t
Hoff. 1
Finally, Shields, 2 at the suggestion of Arrhenius,
studied the hydrolysis of salts, which, as we shall have
to consider later, allows the calculation of the dissociation
constant of water. This constant proves to be the same
as given above.
1 Zeitschr. physik. Chem., 12 , 514 (1893).
2 Ibid., 12 , 167 (1893).
5 & THE THEORY OF ELECTROLYTIC DISSOCIATION .
Let us now discuss one of the most interesting
conclusions from this extremely small water disso-
ciation, namely, the process of neutralization of acids
by bases. The slight dissociation of water is nothing
more than the expression of the fact that H* and OH'
ions possess a very strong affinity for each other, so that
the extent to which they unite to form undissociated
waterjs.scf complete that only the lepeatedly mentioned
very small number of H* and OH' ions is left. If there-
fore 'these* ions meet in any solution in higher concentra-
tions, they, cannot be in equilibrium with one another,
but must continue to unite to form undissociated water
until the product of their concentrations remaining
has reached the value io“ 14 . Therefore upon mixing
equivalent solutions of H’ ions (acids) and OH' ions
(alkalis) the union of these ions to form undissociated
water will set in above all other things, aside from any
further reactions. Whether the anions of the acid and
the cathions of the alkali undergo further chemical action
with one another is of course a question by itself. For
ordinary cases this question is, however, to be answered
in the negative, since, as alluded to above, salts, which
would have to be formed by the combination of these
two kinds of ions, are for the most part strongly dis-
sociated, i.e., consist of ions, so that these ions find no
occasion to form any marked quantities of undissociated
salts. We see then that the essential change taking place
upon mixing acids and bases is the formation of un-
dissociated water by the H* and OH' ions. One con-
clusion from this conception has been known for a very
long time, ever since the investigations of the Russian
THE DISSOCIATION CONSTANT. 59
thermochemist Hess, 1 who made the most startling
discover} 7 , and one at that time inconceivable, that the
heat effect of neutralization of dissolved acids and bases
in equivalent amounts always gave the same value, 13700
cal. per gram-equivalent. On the basis of the dissociation
theory this fact could have been predicted, for in all these
in the ionic sense becomes
K-+OH'+H-+Cl / =K-+Cl'+H 2 0 ,
and leaving out the unchanged substances on the right
and left sides, the ions K* and Cl', we arrive, as you see,
at the above simple equation H* + 0 H / =H 2 0 for the
process of neutralization. A test of the question whether
this heat effect really has the significance of a heat of
dissociation of water, as the simple neutralization equation
represents it, has been possible in another way, namely,
by the investigation of the variation of the water dis-
sociation a with the temperature T. Thermodynamical
considerations give the following mathematical relation
of a and T to the heat of dissociation W (p. 137):
1 dec W
a"df~ 2 RT 2
1 Ostwald’s Illiussiker, Nr. 9, 1S39-1S42.
60 THE THEORY OF ELECTROLYTIC DISSOCIATION .
Kohlrausch and Heydweiller experimentally tested
this variation of the dissociation of water with the tem-
perature by means of the conductivity of pure water, and
found that the heat of dissociation, calculated by the
van’t Hoff equation given above, gave results in complete
agreement with the heat of neutralization as determined
by Hess and Thomsen. (In reality the reverse, which
in principle means the same thing, was done; that is
to say, the variation of the degree of dissociation with
the temperature was calculated by van’t Hoff’s equation,
on the assumption that the heat of neutralization really
represents the heat of dissociation of water.)
Another thermochemical result of Hess is explained
very nicely by the dissociation theory, namely, the
thermoneutrality of salt solutions, or the fact that mod-
erately dilute salt solutions when mixed together give no
heat effect — in other words, show no signs of reaction.
This in spite of the fact that, according to our old views
in such a process of mixing, at least a partial mutual
decomposition of both salts with the formation of new
salts ought to take place. According to the dissociation
theory, however, the ions are for the most part free before
and after the mixing, and therefore no reaction takes
place; for it is extremely improbable that in all these
various cases the heat effects of the reactions taking place
would just compensate each other, making the total
effect equal to zero.
EQUILIBRIA AMONG SEVERAL ELECTROLYTES.
The dilution formula for binary electrolytes in the form
oc 2 c
given above, ^—^== Const., evidently holds only on the
assumption that both ions of the electrolyte are present
in equivalent amounts, which is necessarily correct as
long as no second electrolyte is present in solution at the
same time. It is frequently the case, however, that in a
solution two electrolytes are present which have one of
their ions in common, as, for instance, two acids or two
bases, each of which forms H* and OH' ions respectively;
or a salt and an acid, as sodium acetate and acetic acid;
or a salt and a base, as ammonium chloride and ammonia.
In the last case the ammonium cathion, in the preceding
the acetate anion, are the ions in common. Now in the
same manner as the gaseous dissociation of PCI5, for
example, is affected by the addition of chlorine or PCI3,
just so the addition of a “ like-ioned ” electrolyte must
influence the dissociation of a co-solute, and indeed the
law of mass action gives here, as above, the quantitative
relations. Suppose the two electrolytes to be binary,
and and k 2 the constants which regulate the equi-
librium between the ions and the undissociated portion
6 *
62 THE theory of electrolytic dissociation .
of the electrolytes i and 2 ; then in the common solution
the conditions of the equilibrium for each electrolyte.
Product of the ionic concentrations
Concentration of tne undissociated portion *
must be fulfilled.
If we indicate by c\ and respectively, the total con-
centrations of the two electrolytes and by cti and
their degrees of dissociation, then the concentrations of
the ions not mutual, that is, those which are produced
by one of the electrolytes alone, are equal to aq-Ci and
a 2 -c 2 , respectively; while the concentration of the
mutual ions is made up of those formed from each of
the two electrolytes, and hence is represented by the
expression
(X 1 -C\ +« 2 ' c 2 -
Therefore in the common solution we have the following
relations:
«i-Ci-(n:i-Ci + a: 2 -c 2 )
1— (1— ax) -c x
and
, <*2-g2-(«i-ci + g 2 -C2)
2_ (i-a 2 )-c 2
~^i^ici+a 2 c 2 ),
— — — (otiCi +a 2 c 2 ).
1 — a 2 J
( 6 )
The most important application of this double formula
was made by Arrhenius in his theory of isohydric solutions , 1
which says that upon mixing the solutions of two electro-
lytes having a common ion no change in the degree of
1 Zeitschr. physik. Chem., % 284 (188S).
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. 63
dissociation of either takes place, if the concentrations
of the common ion are the same in both solutions before
mixing.
The correctness of this statement becomes evident
at once when we consider the following example. Assum-
ing that we have a weak acid HA at any concentration c,
then we may write
(H')(AQ
kl ~ (HA) •
Now if we dilute this acid HA by the addition of such
a solution of a second acid in which the concentration
of the H’ ions is just as great as in HA, or, as Arrhenius
puts it, an acid of isohydric concentration, it has no
influence on the concentration of the H’ ions, while the
anions A' as well as the undissociated molecules HA
are both diluted to the same extent. The effect, therefore,
of this dilution disappears in the expression
rTn (AO ,
or in such a case the condition of dissociation remains
unchanged and independent of the mixing ratio ; for with
unchanged H* concentration the H‘ , A' equilibrium
requires that the concentration ratio of anion to undis-
sociated portion be kept the same as in the pure solution
of the acid.
It is clear that we can look upon any mixture of two
acids as composed of such quantities of each pure acid
solution as are isohydric with one another. These
64 THE THEORY OF ELECTROLYTIC DISSOCIATION .
isohydric concentrations may be arrived at through the
following consideration. In the mixture suppose C\ to be
the concentration of the acid HAi, c 2 that of HA 2 , (H")
the total concentration of H* ions, determined by con-
ductivity, catalysis, inversion, or in some other way, and
finally a\ and a 2 the respective degrees of dissociation;
then
£1 —
(H , )(A / x) . aid
(HAi) ^ ; (i-ai)ci
-(HO
1 —<X\
k%=
(HQ (A' 2 )
(HA 2 )
-(HO
a *2 _ m .N «2
(1— a 2 )c 2 ^ J i—a 2
from which
(HO
h '
The sought-for concentrations x± and x 2 of the pure
solutions, whose degrees of dissociation are also a± and
a 2 , are given by the relations:
V <*l 2x l ' _ h 1 -«1
k \ — , X\ — ki
1 -ai
2 >
k 2 —
a^x 2
1 — ol 2
x 2 — h
1 — 0 : 2 ,
: & 2 2 3
or by substituting for a\ and a 2 the values for ki and
k 2 , respectively, found above:
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. 65
or by replacing a with k :
-(HO
and
x 2 = (H*)
(H*) 2
*2 *
in place of which, for small k values, the approximation
usually suffices:
( H ‘) 2 1
Xi = 7 — and
X'l _ &2
a-2 &i
(7)
That is, two acids upon mixing do not influence each
other’s dissociation when their concentrations are very
nearly inversely proportional to their dissociation con-
stants, or the ratio of their concentrations is equal to the
reciprocal ratio of their dissociation constants. Let us
suppose we wish to prepare i liter of a mixture containing
xVmole acetic acid (£ 1 = i.8Xio~ 5 ) and mole glycollic
acid (k 2 ^i$Xio~ 5 ). This can be done, without in-
fluencing the dissociation, by combining solutions of
acetic and glycollic acids having their concentrations in
the ratio x\ :x 2 =i$ 11.8=8-3 :i. Hence we must mix
8.3 volumes of glycollic acid with one of acetic acid of
isohydric concentration (giving 9.3 volumes), and to
fulfill at the same time the above conditions of concentra-
8 3
tion ~ liter of glycollic acid must contain X V mole, i.e.,
0.3 1
be fr^Xo.i =0.112 normal, and — liter of acetic acid
8.3 9-3
must contain yV mole, that is, be 0.93 normal*
66 THE THEORY OF ELECTROLYTIC DISSOCIATION.
The knowledge of isohydric concentrations is important
for the reason that from the conductivities ki and k 2 ,
and the mixing volumes V\ and V 2 , the conductivity k of
the mixture may be very simply calculated thus (by the
rule of three):
*i Fi + k 2 V 2
* = fi+f 2 ■
Or, as Arrhenius expresses this: when two acids are
present in a common solution, the conductivity may be
calculated by introducing into the calculation for each
resulting conductivity the concentrations based on the
assumption that the acids distribute themselves in the
aqueous solvent in the inverse ratio to their dissociation
constants. The agreement of this statement with ex-
perimental results has been proved by Wakeman 1 as well
as by Arrhenius. And it deserves to be mentioned that
r * r • j i - A 2 c
in case of a mixture of acids the expression j ^
derived from the conductivity is not constant, as in the
case of pure acids, but varies with c, so that the study
of the conductivity becomes a valuable criterion of the
purity of such electrolytes.
In order to determine how strongly the presence of a
second acid diminishes the degree of dissociation a x , of
the first acid below the value /?i of the pure solution of the
same concentration, we combine our two equations (6)
(p. 62) into the expression:
<xi
ki (i-oq)
k 2 ol 2 •
(l-«2)
1 Z^it§chr. physik. Chem., 15 , 159 (1894).
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. 67
in which for weak electrolytes it is permissible to write
1 ~ai = i —ct 2= 1, so that we may arrive at the convenient
but nevertheless good approximation formulae:
^2
ai = T--a2 or
R'2 R\
- ( 8 )
Now if w r e are interested in the acid 1, we employ the
equations for the law of mass action, both for the pure
and the mixed acid 1 :
t «i , , N «i 2 / f k 2
kl= ~ o~ == Z. ~~( a l c l +<^2^2) — ( Cl ~r J-C2
1 pi i ~&i i—
^ fa C 2 \
i—ai\ ki Ci) *
Substituting again as above 1 — a'i = i — =1, we
obtain:
/?i 2 £ a ==tfi 2 -£i
/ , k 2 Cq\
V + *1 Cl)’
or
Pi . C 2
= vjl + 7 .
OL\ ^ ki Ci
( 9 )
, v This then is the ratio in which the degree of dissociation
of the acid 1, at the concentration c Vr is depressed by the
addition of c 2 moles per liter of an acid having the dis-
sociation constant k 2 . For the latter acid the analogous
expression holds with interchanged indices.
In order to form an idea of the magnitude of the values
involved, let us consider the case of a mixture of 1 mole
68 THE THEORY OF ELECTROLYTIC DISSOCIATION .
of acetic acid (£1 = 1.8X10 5 ) and 1 mole of cyanacetic
acid (£2 = 37 oXio~ 5 ) per liter. In pure acetic acid we
should have jSi=Vi.8Xio~ 5 = 0.00425; since £- = 205
and — =1, we get
/?i : = \/i + 2 05 = r 4.4 ;
that is, the degree of dissociation is reduced to part,
or from 0.00425 to 0.0003, or from 0.4% to 0.03%. In
general we can see from the equation that the reduction
of fti is greater the stronger the acid (£ 2 ) and the higher
its concentration (c 2 ) is.
To learn the counteraction of the acetic acid on the
dissociation of the cyanacetic acid, we make use of the
analogous expression
^2 -«2 =
44 ---
> £2 C2
.m'the v
>tudy
Here w r e see the -factor under the radical becomes e
to 1+7^=1.0049 (instead of, as before, 206!), or
r 2 . f a
going back of the dissociation — is only about 0.25^
(instead of 1440% as before!); the general comparison
is given by the equation:
EQUILIBRIA AMONG SEVERAL ELECTROLYTES 69
The general result may be summed up in the statement
that in a mixture of acids the acids mutually reduce their
degree of dissociation, but the weaker acid is influenced
very much more strongly. What has been said here about
acids is, by analogy, absolutely true of all other weak
electrolytes, in particular of bases.
From the above it also follows that the farther two
electrolytic solutions are removed from being isohydric
the more also the conductivity of their mixture must be
reduced as compared w T ith that of the unmixed solutions;
for the minimum o of the mutual influence corresponds to
the isohydric state. So having a solution a of an electro-
lyte, it is possible to determine the isohydric condition
of another solution b having ions in common with it, by
adding the solution a to different concentrations of b.
That concentration of b is isohydric with the given solution
a, which by the addition of the latter brings about the
maximum increase in conductivity. This deduction
may under circumstances be useful for determining
the degree of dissociation of a, when that of b is known
and a is not directly determinable . 1
. In a precisely similar manner the mass-action formulas
for any more complex mixtures of electrolytes may be
derived, as Arrhenius has made clear in his studies of the
equilibrium relations between electrolytes . 2 Let the dis-
cussion of a simple special case suffice here, a case of ex-
treme importance to analytical chemistry, namely, that of
two electrolytes, one very strong, the other very weak,
1 Compare W. Bonsdorff, Ber. d. deutsch. chem. Ges., 3 G, 2322 (1903) ;
Zeitschr. anorg. Chem., 41 , 132 (1904).
2 Zeitschr. physik. Chem., 5 , 1 (1890).
THE THEORY OF ELECTROLYTIC DISSOCIATION.
so that by their mixture the dissociation of the strong
electrolyte is only slightly influenced, while that of the
weak is affected all the more.
This case is realized in general whenever we mix a
weak acid or a weak base with one of its neutral salts
(strongly dissociated according to the rule, p. 26) or with
a strong acid or base respectively. Then by equation
(6) (p. 62), designating the weak electrolyte by 1 and the
strong by 2,
£1 =
ai-Ci’(ai-Ci+a2’C2)
(1 -ai)-ci
i-«i
(a 1 c 1 +a 2 c 2 ),
the degree of dissociation <*i is greatly reduced according
to the measure of the concentration c 2 .
In order to obtain an approximation for this reduction,
let us, as before, but with even greater exactness, write
1 — #1 = 1, for the degree of dissociation of our weak
electrolyte 1 in unmixed solution. This degree of dis-
sociation, small by assumption, is made even smaller by
the mixing. Further, for the sake of simplicity we shall
assume that 0:2=1, or that the dissociation of the strong
electrolyte is practically complete. Then we may also
write our equation:
h =<*1 +£ 2 ) =oti 2 Ci +aic 2 .
Again, if the concentrations ci and c 2 are of the same
order of magnitude, i.e., the concentration of the strong
electrolyte is not very much smaller than that of the weak,
we may in the latter expression drop the first summation
as compared with the second . without introducing any
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. 71
great error, because a x , the degree of dissociation of the
weak electrolyte in the mixture, is a small magnitude,
hence its second power represents a magnitude of the
second order. It follows then that approximately
r • h
Ki~o^i m C2, i.e., ct r i = — ,
C2
*and the concentration etjCi of the non-mutual ion is
aici=h— , (n)
C 2
or in words: the degree of dissociation a x of the weak
electrolyte in the common solution of both electrolytes
is directly proportional to the concentration of the strong
electrolyte and inversely proportional to its dissociation
constant. In order to point out the significance of these
relations by way of several examples, let us consider the
cases mentioned above of equivalent mixtures of acetic acid
and alkali-acetate or of ammonia and ammonium salts;
then for a x w r e must introduce the degree of dissociation
of acetic acid and ammonia respectively, for the constant
ki the value 1.8X10 -5 and 2.3 Xio -5 respectively. We
find thus that in pure 1 -normal solutions of acetic acid
and ammonia the degree of dissociation is respectively
0.4% and 0.5%, while the same upon addition of 1-
normal acetate and ammonium salt is depressed to
0.0018% and 0.0023% respectively. These degrees of
dissociation in the mixtures express at the same time,
in the case of the acetic acid, the concentration of the H*
ions, in the case of the ammonia, that of the OH' ions,
72 THE THEORY OF ELECTROLYTIC DISSOCIATION.
and give us a measure of how very greatly the acid and
basic properties, based on the concentration of these ions,
are diminished. In the case of ammonia this fact was
made use of long before its theoretical explanation was
known, namely, in reducing by the addition of ammonium
salts the power of ammonia to precipitate magnesium
ions as magnesium hydroxide, or, practically speaking,
counteracting it altogether. Likewise the reduction of
the concentration of the sulphur ions in hydrogen sulphide,
by increasing the concentration of H' ions through the
addition of strong acids, is made use of in analysis to
counteract the power of H2S to precipitate zinc. The
equilibria appearing in connection with precipitating
reactions will be further discussed later on. This driving
back of dissociation, Arrhenius also proved experimentally
for formic acid and acetic acid. As previously alluded
to (p. 5), the inversion of cane-sugar is catalytically
accelerated by acids, in proportion to the H* ion con-
centration of these acids, which is shown by a compari-
son of the catalytic action of varying acid concentrations.
The following table gives the value of this catalyzing
constant for several such acids and the influence upon it
of additions of neutral salts.
p indicates the reaction-velocity constant, i.e., the
quantity of sugar inverted per minute, when the sugar
possesses during the minute the concentration 1. The
measurements were carried out at 54 0 , at which tem-
perature k (acetic acid) =1-615 Xio" 5 an d ^ (formic acid)
= i.83Xio - 4 , for calculating the H* concentration.
For ¥ V norma l HC 1 it was found that <o=4.69Xio~ 3 ;
this velocity of inversion is therefore brought about by
EQUILIBRIA AMONG SEVERAL ELECTROLYTES . 73
an H‘ concentration = ^=0 0125 normal, since HC 1 in
-gVN solution practically may be considered as completely
ionized.
A 0.25-N acetic acid has, since £ = 1.61 5Xio -5 ,
the H* concentration (H*) 2 = &Xo.25 or (H’) =
v / o.25Xi.6i5Xio“ 5 = o.oo 2 normal, hence we should
0.002
have /)=4.6 oXio~ 3 — ! — — = o.7aXio“ 3 ; the value ob-
r ^ y 00125 9
served was p=o.j$Xio~ 3 : likewise for 0.25-N formic
acid we calculate 0.25 X 1.83X1 o" 4 == 0.00678
o 00678
and £=4.69X10 =2. 54Xio“ 3 , while 2.55X10 3
was the value found. In exactly the same manner the
(H‘) values, and from these the t o calc . values, have been
derived for the following mixtures, and the good agreement
of Pcaic. and ^obs. proves that the basis of the (H‘) calcu-
lation in the above equation agrees with the facts.
0.25-N Acetic Acid 4 - c-Normal Sodium Acetate.
(Arrhenius, 1889.)
c—o
0.0125
i
0.025 !
i
0.05
0.125
0.25
IO 3 j 0 obs. =0.75
10 3 />calc. =0.74
0.122
O.I29
0 0
0 0
d o'
0.040
0.038
0.019
0.017
0.0105
0.0100
0.25-N Formic Acid + c-Normae Sodium Formate.
c— 0
0.025
0.1
0.25
ioVoba. =2.55
0.72
0.24
0.118
IO^calc. =2.54
o -75
0.24
0.117
Another special case of electrolytic equilibria is that
74 THE THEORY OF ELECTROLYTIC DISSOCIATION
of a mixture of two electrolytes with common ions, having
equal strengths (k 1 = k 2 ), as seems to be approximately
the case with analogous salts. Then by equation (6)
(P- 62)
k\ = k 2 —
(aiCi -ha2C 2 )oLiCi
(1 —ai)ci
(a'iCi+a2Co)o , 2 C2
(1 —a2)c2 9
that is,
a\ a.2 k
1 — a'x 1 — (x.2 (XiCi+a.2C2 9
from which it follows ai=a 2 ~a and = — , — , or
1 —a Ci ~ f c 2
in words: the degree of dissociation in mixtures of
electrolytes of like strength is equal to and of the same
value as that which would correspond to each alone for
the concentration (ci+c 2 ).
From the theory of the electrolytic equilibria relations
we can derive the explanation of a whole series of well-
known manifestations. Theoretically in every case in
which two electrolytes, that is their four ions, are present
in the same solution, there must be formed by the inter-
action of these ions some certain quantities of the four
possible undissociated substances. So, for example, upon
mixing KC1 and NaBr, there are present in the solution, in
addition to these two undissociated salts, certain amounts
of NaCl and KBr, resulting from the reciprocal interaction
of their ions. Since, however, the tendency of all these
four substances to dissociate is great, there cannot be
formed any appreciable quantities of the new undisso-
ciated substances. It is a very different situation if it
so happens that one of the four possible substances
possesses a very slight tendency to dissociate, or the
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. 75
reverse as we had probably better say here, in case ex-
ceptionally strong atomic affinities are in action between
any two of the ions participating in the equilibrium.
This is, for instance, the case when we bring together the
strongly dissociated substances HC 1 and Na-acetate.
The possibility is then at hand that NaCl and H-acetate
will be formed simultaneously; however, while NaCl is
strongly dissociated, there exists a marked tendency to
combine between the ions H* and acetate', which causes
almost all of these ions to unite to form undissociated
acetic acid, and results in a disappearance from solution
of the particular ions as such. As one sees, this view
contains the theory of the general experience that strong
acids “ liberate ” the weak acid from the salts of weak
acids, and likewise of course strong bases liberate the
weak base from the salts of weak bases, or, in the language
of the dissociation theory, transform their ions into the
undissociated state. Wherever, then, an H' ion meets
the anion of a weak acid, or an OH' ion the cathion of
a weak base, the opportunity is made use of for both
these ions to pass from the ionic state into undissociated
substances. When we, for example, “set free” ammonia
(£=2.3 Xio -5 ) from the strongly dissociated ammonium
salt by the addition of strongly dissociated alkali-hydrox-
ide, or carbonic acid (k = ^.o4Xio~ 7 ) from strongly
dissociated sodium carbonate by strongly dissociated
HC 1 , or hydrocyanic acid (k = i:^Xio~ 9 ) from strongly
dissociated potassium cyanide by strongly dissociated acid,
etc., we are doing nothing else than giving the ions of these
weakly dissociated electrolytes the opportunity to unite
and form uhdissociated electrolytes. Writing the equation
7 6 THE THEORY OF ELECTROLYTIC DISSOCIATION .
for any such reaction, for example:
K' + CN' -f- H* + CY = K“ + Cl' +HCN,
we see that, similar to the case of neutralization, the
unchanged ions remaining on both sides may be omitted,
and the formula for the reaction becomes :
H* + CN' = HCN.
We have here evinced, then, a very striking analogy to
neutralization, or, as we must express it in the sense of
the ionic theory, the analog}' of the formation of undis-
sociated water from its ions to the formation of a weakly
dissociated electrolyte (HCN, H 2 C0 3 , NH 4 OH, H 2 S, etc.,
etc.) from its ions, or, put in the old way, to the liberation
of weak acids or bases from their salts.
The old formulation, still employing the last example,
that potassium chloride is produced from potassium
cyanide by the action of hydrochloric acid, is, strictly
speaking, a distorted mode of expression, inasmuch as
the constituents of potassium chloride continue in the
same condition (ionic) after the reaction as before. The
really essential part of the change is the formation of the
undissociated weak electrolytes, precisely as it is the
formation of water in neutralization.
HYDROLYSIS.
In the cases of aqueous solutions discussed thus far, we
have left out of consideration altogether that there is.
EQUILIBRIA AMONG SEVERAL ELECTROLYTES .
77
peculiar to the solvent, water, as we saw above, a very
small but nevertheless measurable and exactly known
dissociation into the ions H* and OH 7 . We have, then,
still to discuss how far and in what cases we are justified
in assuming a participation of the water in the equilibrium
between the electrolytes, and what may occur under
those circumstances. For instance, in the simplest case,
the solution of a strong salt such as NaCl, there is the
possibility of the Na* ions combining with the OH' ions
of the water to form undissociated NaOH, and the
Cl' ions with the H* ions of the water to form undissociated
HC1. We know, however, from the conductivities,
freezing-points, etc., that neither of these two new com-
pounds possesses to any sensible degree the tendency to
assume the undissociated state, but that, on the contrary,
they split up to a far-reaching extent into their ions. In
consequence of this, neither of the ions of water is to any
appreciable extent taken into custody by the ions of such
a salt. The matter takes on a different aspect when,
for example, the strongly dissociated salt of a very weak
acid or base is involved; in such cases the ion of the
weak acid or base present in the salt in large concentration
finds an opportunity to unite with the ion of water neces-
sary to form the weak acid or base. What is more, we
are in position to determine, on the basis of the law of
mass action, the extent to which this can take place.
Taking under consideration a i -normal solution of potas-
sium cyanide in water, we must have in this, in addition
to the equilibrium between K* and CN' ions and undis-
sociated KCN, the following three equilibria;
73 THE THEORY OF ELECTROLYTIC DISSOCIATION .
1. K* ions and OH' ions (of water) with undis-
sociated KOH;
2. CN' ions and H* ions (of water) with undis-
sociated HCN;
3. H* ions (of water and the HCN formed) and
OH' ions (of water and the KOH formed)
with undissociated water.
The K",OH' equilibrium, as well as the K‘, CN', cor-
responds to strongly dissociated substances, while for
the H‘, CN' equilibrium we have the equation (see pp. 63
and 55)
_ (H-)-(CN')
(HCN)
1.3X10- 9 ,
and for the H*, OH' equilibrium
k w = (H*) • (OH') = 1.2 Xio~ 14 .
Suppose this action of the water, the so-called hydrolysis,
the result of which consists in the splitting up of part of
a neutral salt into acid and base according to the equation
KCN -f H 2 0 = KOH + HCN,
has taken place to the extent x, so that x represents the
fraction of each mole of neutral salt which has been split
up in this way into base and acid. If c stands for the
total concentration employed, then, according to the
statements made, there would be present in the “ hydro-
lytic ” equilibrium
ivcKOH -h^cHCN 4- (1 -#)cKCN,
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. 79
Applying to these quantities the equilibrium equations
of hydrocyanic acid and of water,
i- We may practically identify the concentration of
the undissociated HCN with the total concentration of
the same equal to x-c, for hydrocyanic acid is an exceed-
ingly weakly dissociated acid, whose degree of dissociation
in addition is reduced by the presence of the many cyano-
gen ions of the strongly dissociated KCN.
2. The concentration of the CN' ions we may without
marked error place equal to the concentration (i — x)c of
the undecomposed KCN, since, for the reasons named,
the cyanogen ions arising from HCN must be exceedingly
few.
3. The H* ion concentration, which is here required
for the H‘,CN' equilibrium, we obtain with the aid of the
water equilibrium, since we know the concentration of
the OH' ions. This is practically equal to the total
concentration of the (strongly dissociated) KOH, that
is =x-c. Now since
(H*) • (OH') = k w or =
we can introduce all the values into the H*,CN' equilibrium
equation and get
(H-)-(CN') 1 — x
k ‘~~ (HCN) “ x-c ~ kw '
K x 2 -c '
kg 1 — x
v.- (**)
In the form
So THE THEORY OF ELECTROLYTIC DISSOCIATION.
the analogy with the dilution law is very evident, and this
hydrolytic dilution law can also be formulated in the
words :
(Cone. Acid) * (Cone. Base)
(Cone, non-hydrolyzed Salt)
= Hydrolytic Constant,
just as we have
(Cone. Cathions) ■ (Cone. Anions)
(Cone, undissoc. Salt)
= Dissociation Constant.
Herewith we have an expression consisting entirely
of known factors, namely, the known total concentration
c and the constants of hydrocyanic acid (k 8 = i.^Xio~ 9 )
and of water (4 w = i. 2 Xio' 14 ), which enables us to
calculate the degree of hydrolysis (x).
Solving this equation for x, we get
For the cases in which the ratio k u . : k s is small as
compared with i, i.e., the constant of the w r eak acid is
much greater than the water constant, this equation may
be simplified without great error to the approximation
equation :
x= ^lvt (I3)
The equation teaches us that the degree of hydrolysis is
dependent on the ratio of the dissociation constants ol
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. Si
the weak acid, whose salt we are considering, and that
of the water. Hydrolysis increases, therefore, the weaker
the weak acid or base contained in the salt is. In a
qualitative way one can get a very good picture of the
relations by the following considerations.
The H* ions of the water act upon the weak anions of
the salt with the formation of free undissociated acid;
the place of the acid anions thus consumed is taken in
equivalent amount by the OH' ions of the water that were
formerly bound to the H' ions, producing a definite OH'
ion titer of the solution. Thereby, however, the concen-
tration of the H* ions (on account of the H* , OH' equi-
librium, that must always be maintained) is reduced
to such a small amount that no further free acid can be
formed by their action. By the production, then, of
the OH' ions or the free base the continuation of the
hydrolysis is retarded (in that these ions suppress the
hydrolytic action of the H' ions) and is finally brought
to a standstill, this standstill setting in the later the less
H' ions the acid anions require for the formation of
undissociated acid, i.e., the weaker the acid is.
The same is true of course, mutatis mutandis, for the
salts of very weak bases, in which case the OH' ions of the
water are the hydrolyzing and the H* ions the retarding
ones.
Starting with a salt hydrolyzed to the amount x, then,
the concentrations (acid and base) are equal and equiv-
alent, and the above equation holds, as Shields 1 demon-
strated for KCN:
1 geitscfrr. p&yslk- Chenfc, IS, 167 (1893),.
82 THE THEORY OF ELECTROLYTIC DISSOCIATION.
Potassium Cyanide.
(Shields, 1893.)
c
lOOX
(l-*)
0.947
°-3 I %
O.9 XlO“ 5
0-235
0.72
I. 22 XIO -5
0.095
I . r 2
i . 16 X 10— 5
0.024
2.34
i
1.3 X10- 5
Mean: i.iXio~ 5
The hydrolytic constant, which for immediate purposes
we can derive on the basis of the law of mass action
without any knowledge of the dissociation theory, never-
theless represents the ratio k w : k 8 according to this theory,
and therewith makes it possible to obtain the constant k 8
of the weak acid, by means of (12), from the water con-
stant ^ = 1.2 Xio -14 by dividing the same by the hydro-
lytic constant. Accordingly, for HCN the same becomes
1.2X10’ 14
1 .1 Xio“ 5
= 1.1 Xio
-9
while Walker found by direct
measurement and in close agreement with it the value
1.3X10- 9 . Similar to the significance given to the dis-
sociation constant (p. 46), we may formulate the physical
sense of the hydrolytic constant so that it signifies the
half of that concentration at which the salt is just hydro-
lytically decomposed one half, or (in case the degree of
hydrolysis is small) the root of the hydrolytic constant of
the concentrations of the products of hydrolysis in the
i-N salt solution (when the salt contains only one very-
weak ion).
It is possible;' then, to obtain inversely . from the table
EQUILIBRIA AMONG SEVERAL ELECTROLYTES &3
(p. 55) the hydrolytic constant by dividing the water
constant 1.2 Xio -14 by the dissociation constant given,
that is, the degree of hydrolysis of the i-N salt solution
according to (13) by dividing 1.1X10" 7 by the root of
the dissociation constant.
The constant
(Acid) * (Base)
(Salt)
W alker 1 determined
experimentally on mixtures of the very weak base urea
with hydrochloric acid, by measuring the velocity of
inversion p produced on the one hand by the pure acid
(po) and on the other by the urea to which acid had been
added. Then represents the fraction still having
inverting action, and 1 tih- e P art th e acid bound as
a salt of urea, as well as the urea itself thus bound, so that
c ~(^ ~y S j £i yes f ree urea which, for the concentration
c employed, is left after the formation of salt; conse-
quently we should have
Hydrolytic Constant.
1 Zeitschr. physik. Chem., 4 , 319 (1889).
&4 THE THEORY OF ELECTROLYTIC DISSOCIATION.
Normal Hydrochloric Acid + c-Normal Urea.
(Calculated after Walker, 1889.)
c
9
PO
Cone, of
Free HC1.
1- — =
<00
Cone, of
Salt
Formed.
«-.+*-
9 0
Cone, of
Free Urea.
Hydrol.
Const.
0
0.0031 5 = ^3
I
—
—
—
°-5
0.00237
o -753
0-247
0.253
0.77*
1
0.00184
0.585
0-415
0-585
0.82
2
0.001 14
0.36
0.64
I.36
o-77
3
0 . 00082
0.26
0.74
2.26
0.80
4
0.0006
0. 19
0.81
3-19
o-75
Mean: 0.78
In a similar manner Walker’s measurements (re-
calculated) give the following hydrolytic constants:
Thiazole o . 00367
Glycocoll o . 00425
Asparagine 0.0079
Thiohydantoin 0.0127
Aspartic acid 0.0137
Acetoxime o . 0196
Acetamide 4.0
Propionitrile 6.7
Thiourea 10.5
from which the dissociation constants given on p. 55
for these basic-acting substances were calculated.
Hydrolysis is outwardly recognized by the fact that
a salt of neutral composition reacts in aqueous solution
either acid or alkaline and not neutral, i.e., that the forma-
tion of H' or OH' ions from the water is induced. In
this particular the reaction of hydrolysis may possibly
be most clearly represented thus, that the particular salt
by means of its one weak ion acquires the opposite ion of
EQUILIBRIA AMONG SEVERAL ELECTROLYTES . $5
the water for the formation of the undissociated compound
and thereby disturbs the H* , OH' equilibrium. Since
this equilibrium, in consequence of the presence of water,
must be maintained, there appears in place of the water
ion which disappeared a quantity of the other water ion,
to be calculated according to the equation
(H0 = ^g 7 j and (OH , ) = ^- respective!}'.
As a result the salt of a weak base reacts acid, and that
of a weak acid alkaline.
From the fact of this reaction it follows, on the basis
of the law* of mass action, that hydrolysis in the case of a
weak base is reduced by the addition of H* ions, in the
case of a weak acid by the addition of OH' ions, for both
these kinds of ions are reaction products of hydrolysis,
and the increasing of the concentration of reaction prod-
ucts always acts against the progress of the reaction.
We may also picture this to ourselves thus: start with
the consideration of the H‘ , OH' equilibrium and look
upon the addition of OH' ions (in the form of any strong
base) as a forcing back of the H* ion concentration of
the water. This works against the reaction of these H*
ions with the weak anion of the electrolyte, because the
quantity of the undissociated weak electrolyte produced
by the hydrolysis is proportional to the concentration of
the hydrogen ions which come into consideration for this
equilibrium. The same is true also, mutatis mutandis ,
of the hydrolysis of a salt of a weak base upon the addition
of H’ ions. These deductions from the law of mass
86 THE THEORY OF ELECTROLYTIC DISSOCIATION
action may likewise easily be confirmed at the hand of
experience. If, for example, we add strong caustic
alkali, i.e., increase in this way very considerably the
concentration of the OH' ions in a solution of potassium
cyanide or ammonium sulphide, both of which reveal
their hydrolysis not only by their alkaline reaction but
also by the odor of undissociated hydrocyanic acid and
hydrogen sulphide respectively, then the forcing back of
the hydrolysis manifests itself in the disappearance of
the odor of hydrocyanic acid and hydrogen sulphide
respectively. Again, if we add strong acid to a solution
of ferric chloride or iron alum, which react acid in conse-
quence of hydrolysis and at the same time show the brown
color of the undissociated ferric hydroxide (in colloidal
solution), the brown color of the undissociated ferric
hydroxide disappears more and more, giving place to the
colorless condition belonging to the ferric ions. Gen-
erally speaking, by forcing back hydrolysis by means of
OH' ions or H‘ ions, those properties of a hydrolyzed
solution that belong to the undissociated component
disappear.
As the equilibrium equation of hydrolysis shows, the
hydrolytic decomposition can not only be forced back-
ward by the addition of either H' or OH', but also by
the addition of the undissociated product of hydrolysis.
Thus, for instance, the acid reaction of a solution of
aniline hydrochloride is destroyed by an excess of aniline,
and Bredig 1 was enabled by this device to measure the
ionic mobilities of salts subject to hydrolytic decomposi-
tion.
‘ 1 Zeltschr. physik. Chem., 13 , 214 (1894).
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. S;
In reality, according to the theory, all sails should be
subject to hydrolytic decomposition, and the equation
(13) (see p. 80) for hydrolysis enables us to determine
quantitatively the degree of decomposition as soon as
we are in possession of the dissociation constant of the
weak constituent of the salt. It turns out that the degree
of hydrolysis of weak electrolytes, whose dissociation
constant is of the order of magnitude of that of acetic
acid, is still exceedingly slight, so that a 0.1 -normal
solution of sodium acetate is hydrolyzed only 0.008%, 1
as shown by the investigation of Shields. 2 He measured
a reaction velocity which is proportional to the concen-
tration of the OH' ions, namely, the saponification of
ethyl acetate, whereby he determined the OH' ion con-
centration and therewith the hydrolysis of salts of weak
acids. His results are contained in the table, p. 91, as
well as Walker’s 3 calculated degrees of hydrolysis, which
he obtained by means of the dissociation constant of the
weak acid, this constant having been determined by
conductivity measurements.
As can be seen, noteworthy degrees of hydrolysis are
to be expected only in the case of salts of extremely w r eak
electrolytes, such as those enumerated in the table on p.
55. All the salts of the acids and bases mentioned there
1 According to equation ( 13) :
a/JL IO %W o~^6 7 X io-» = o.8 X 10-*.
y 10 i.sxio - 5
2 Zeitschr. physik. Chem., 12 , 167 (1S93).
*Ibid., 32 , 1 37 (1900), and Joum. Chem. Soc., 77 , 3 (1900).
88 THE THEORY OF ELECTROLYTIC DISSOCIATION.
are hydrolyzed to such an extent that one can demonstrate
by indicator reactions the presence of measurable quan-
tities of OH' or H* ions. One frequently meets with
the view that the determination of this OH' or H*
concentration, or, what is the same thing, the alkali
or acid titer, is possible by means of alkalimetric or
acidimetric titrations respectively. But this is impossible,
for the reason that the. ionic reactions take place with
an immeasurable velocity, and in consequence, as the
H* or OH' titer in the hydrolyzed solution changes, new
equilibria of the various ionic concentrations establish
themselves at once. An illustration, at the same time of
great importance to the chemistry of our daily life, will
help to make the case clear. Consider a solution of
borax, which on account of the weakness of boric acid
(see p. 55) is hydrolyzed and hence gives an alkaline
reaction; in this for the moment we may attempt to
convert these hydroxyl ions into water by the addition
of hydrogen ions. This would at once raise the H* ion
concentration to a greater value than is in keeping with
the equilibrium H' , H2BO3' of boric acid. The excess
of H* ions would then be taken up again by the borate
ions forming undissociated boric acid, whereupon a
fresh quantity of hydroxyl ions would again have to be
formed, owing to the H* , OH' equilibrium, or, in other
words, the alkaline reaction, that we attempted to destroy
by the addition of acid, persists in spite of it. In fact,
this continues as long as appreciable quantities of borate
ions are present in the solution, sufficient to take pos-
session of the H' ions added with the acid. On this
behavior is based the possibility of choosing borax for
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. 89
neutralization, as is not infrequently done in alkalimetry,
instead of alkali-hydroxides. Likewise potassium cyanide
might be used, but for other reasons it is not feasible.
The application of soap, soda, and borax in the house-
hold is also essentially based on the fact that these Xa
salts of very weak acids, as a result of hydrolysis, give
solutions of appreciable but yet of^ sj^h^sma^QEL', con-
centration that l tfiffi£^|Bti^®t|(iai fisl |^il ; innjDt5hg,
though still stimcrent ro make their swelling and tat-
solvent action effective.
mm
i is. ^
d, without stliei-efore
must be still more strdf
the concentration of the H' cr OH' ions becoming greater
than in the previously discussed case. The mass-action
equation for the hydrolysis of such a salt can likewise be
very simply derived. Take a salt such as ammonium
cyanide or aniline acetate of the concentration c , and
indicate, as before, the degree of hydrolysis by x, that is,
the quantity of free acid and base formed by the water
per mole of salt, then in the hydrolytic equilibrium we
have:
x-c free base free acid + (i —x)c non-hydrolyzed salt.
Indicating further the dissociation constant of the
base by k b , of the acid by k 8 , and the ionic product of
water by k w (at ordinary temperature io~ 14 ), then the
following conditions of equilibrium must be fulfilled at
the same time:
i.
For the base:
(Cathions) * (OH') _
(Undissoc. Base) bl
t)0 THE THEORY OF ELECTROLYTIC DISSOCIATION.
n
For the acid:
(Anions) • (H‘)
(Undissoc. Acid)
3. For the water: (H*) -(OK r ) = k w .
On the strength of similar considerations as above
(p. 79), we may place the concentrations of the undisso-
ciated base as well as the undissociated acid equal to their
total concentration (x-c), and further, as experience has
shown (of the four electrolytes here present only the
neutral salt is to be considered as strongly dissociated),
we may with useful approximation assume the concen-
tration of the basic cathions as well as of the acid anions
as equal to the concentration of the salt (1— x). We
obtain then
(OH')-(i -afl-c :
x-c
(H')-(i —x) c
and by multiplying these two values, the relation
or (compare pp. 79, 80)
k w (Cone. Acid) • (Cone. Base)
k^kT (Cone. Salt) 2 ’* * (l5)
after having introduced for the product (H*)* (OH') its
value k w . We get for the hydrolysis of such a salt, consisting
of two weak components, the interesting result that the
hydrolyzed portion is entirely independent of the concen-
tration of the salt, since this concentration falls out of the
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. 91
final equation. The correctness of this relation has
been experimentally confirmed by Walker at the instiga-
tion of Arrhenius. The accompanying table on hydroly-
sis contains these results taken from the fundamental
research of Arrhenius . 1
Degrees of Hydrolysis.
(Shields, 1893, and Walker, 1900.)
Salts of Weak Acids.
Shields, Found.
j _ _ . '
' Walker, Calc.
0 t-ML Sodium acetate
0 . coS%
0.06
0.1-N. Sodium bicarbonate
0 i-N. Sodium hvdrosulphide
0.14
0.84
°3
0.96
0 i-N. Sodium metaborate
;
0.1-N. Borax =2NaB0od-B o 0 3
0.1-N. Sodium cyanide \
; about 0.5
0 . i-N. Potassium cyanide J
0.1-N. Sodium phenolate )
1 . 1
! ;
0. i-N. Potassium phenolate J
3 *°
3 -o
Salts of Weak Bases.
Vgo— N. Aniline chlorhydrate 2.6%
V32— N- ^Tohiidine chlorhydrate. .. . 1.5
1 / 32 -N. 0-Toluidine chlorhydrate. ... 3.1
1 / 33 -N. Chlorhydrate of urea 95-°
Aniline Chlorhydrate.
(Bredig, 1894.)
- T
C
100#
t i — x ^Aniline
c x 2 ~~ k w
3 2
2.63
45X10 3
64
3-9°
40X10 3
128
5-47
40X10 3
256
7.68
40X10 3
512
10.4
42X10 3
1024
14.4
42X10 3
1 Zeitschr. physik. Chem. 7 5 , 18 (1890).
92 THE THEORY OF ELECTROLYTIC DISSOCIATION .
Aniline Acetate.
(Arrhenius and Walker, 1890.)
100X
12.5
54-6
i 25
55-3
5 °
56*4
100
55 - 1
200
55-6
400
55-4
Soo
5^-9
Mean: 55. 7 1
Of inorganic salts those of the following weak cathions
show hydrolysis with acid reaction 2 when associated
with strong anions:
■ Be'*, Hg 2 ” Hg“, Cir*, Al**‘, Cr***, Fe***, Mn***, Sn’*,
Sn****, Sb-, Bi*“, U:::.
With weak anions we usually have great insolubility,
the formation of basic salts, or inappreciable dissociation
(Hg**). Alkaline reaction is shown by the weak anions,
H 2 B0 3 ', P0 4 '", HPO4", HS', S", CO3", ’HC0 3 ',
Cr0 4 ", Si0 3 ", SO/', CIO', N0 2 ',
w r hen associated with strong (alkali) cathions; with weak
cathions we have in all cases insolubility.
k w 1.2 x 10 14
H'ka 4.9 X IO —10 Xl.8X io~ 5 I ' 4 '
Compare equation (15), p- 90.
2 Concerning the quantitative relations, compare the thorough and
comprehensive study of H. Ley, Zeitschr. physik. Chem., 30 , 193 (1899).
EQUILIBRIA AMONG SEVERAL ELECTROLYTES . 93
The other question, whether such a salt reacts alkaline
or acid, may according to the above mathematical re-
lations for k b and k s be very easily decided. If we recall
that a neutral reaction means the same as the presence of
equivalent amounts of H* and OH' ions, or, in the form
of equations,
(H-) = (OH') or
then by analogy the basic reaction must be formulated
thus:
JSl <t
(OHO ’
and the acid reaction:
(OHO ’
and so we may express the value
(HQ
(OH')
according to equation (14) (p. 90) in terms of the ratio
k 8 -
for, as we see.
h_ (HQ
K (OHO
(16)
Hence we obtain acid reaction when, as with aniline
acetate^
k s > k b/i
94 THE THEORY OF ELECTROLYTIC DISSOCIATION.
basic (alkaline) reaction when, as with (NH 4 ) 2 C 03 or
(NH 4 ) 2 s,
k& ^ kb j
and neutral reaction when, as is approximately the
case with (NH 4 ) 2 C 2 H 3 02 ,
k s k' 0
The hydrolytic relations of a salt with two weak ions
will also establish themselves if we add to a solution of a
salt of one-sided weakness a salt that has a second w T eak
ion of opposite nature. To cite an example, consider
the hydrolysis of ammonium chloride, which is limited
upon reaching a certain (in this case very small) H’ ion
concentration. If we add another salt with a very w T eak
anion, for example KHS or K 2 C0 3 , then its anion HS',
or C0 3 ", will consume the H* ions, formed by the hy-
drolysis of the ammonium chloride, for the production
of the undissociated acid H 2 S or H 2 C0 3 respectively.
Herewith the previously existing check, which interfered
with the progress of the NH 4 C1 hydrolysis into NH 3 +HC1,
is removed. The result is that the first NH 3 -producing
hydrolysis goes on and the newly formed H' ions continue
to be bound by the HS' or C0 3 " ions respectively, etc.,
so that the undissociated products of hydrolysis of a
w T eak pair of ions must reach much higher concentrations.
In the case selected this becomes very evident; for w hil e
a solution of NH 4 C1 is so little hydrolyzed that there is no
sign of the odor of ammonia, the odor is in evidence at
once on the addition of K 2 C0 3 or NaHS solution. In
the latter case the odor of H 2 S also appears as an indica-
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. 95
tion that the HS' ions have executed their H '-binding
action.
Such action is also made use of in analysis, for instance
in the precipitation of Al‘*‘ and Fe'“ by means of an
acetate (see.p. 142).
The hydrolytic relations may in addition be viewed
from another side, by considering the possibility of
arriving at and examining the equilibrium of a reaction
not only by starting with the reacting substances (salt +
water), but also by starting with the products of the
reaction (acid+base).
We arrive at the equilibrium in the latter way by adding,
we shall assume gradually, an equivalent amount of
strong base to, for example, a weak acid (dissociation
constant = k 8J ionic concentration in pure solution =\/&«,
equivalent for anions and H’ ions). Thereby we disturb
the equilibrium of the weak acid, for we consume the
H' ions of the same, which must form undissociated
water with the OH' ions of the added base. In conse-
quence of which, in order to maintain the ionic product
k S} a quantity of acid anions must be produced equivalent
to the consumed H‘ ions, and these in turn again reduce
more and more the H' ion concentration, on account of
the dissociation equilibrium of the weak acid, until
finally this has become as small as is demanded by the
H*, OH' equilibrium.
AVIDITY.
The phenomenon of hydrolysis, discussed in the
preceding pages, is fundamentally nothing more than
9 6 THE THEORY OF ELECTROLYTIC DISSOCIATION.
an interesting special case of a general and important
equilibrium problem. Long before the time of the
dissociation theory, this problem had been investigated
thermochemically by Thomsen 1 and volume-chemically
by Ostwald, 2 as the distribution of a base between two
acids and an acid between two bases, and was termed by
the former the avidity of acids and bases.
In order to dispose of the theory of the question, let
us consider the case of having mixed in a liter of solution
b moles of a strong base (BOH),
ci moles of the acidx (HAi), and
c 2 moles of the acid 2 (HA 2 ),
and let b <Ci+c 2 , i.e., the amount of the base is insufficient
to neutralize both acids. If now we call x the fraction
of each mole of base which reacts with the acidi, then
(i —x) is evidently the fraction remaining for the acid 2 .
In the resulting equilibrium there will be formed
and be remaining:
Salt BAi : bx ; Acid HAi : Ci — bx;
Salt BA 3 : 6(i -*); Acid HA 2 : c 2 -b( i -*).
If both acids are weak, and both salts, as is usually
the case, almost completely dissociated, then the
ionic concentration (A i)=bx, (A 2 ') = b(i —x), and the
remaining portions of the acids may, on account of the
presence of their salts (see pp. 70, 71), be considered
1 Thermochemische Untersuchungen. Leipzig, 1884.
2 Journ- prakt, Chem. (2), IS, 328 (1878).
EQUILIBRIA AMONG SEVERAL ELECTROLYTES . 97
as essentially undissociated; their small hydrogen ion
concentration (H*) in the solution has of course the same
value. Accordingly, the dissociation constants ki and k 2
of the acids are represented by the following expressions:
(H-)(AiQ (HQ-to
1 (HAi) d-bx’
, (HQ(A 2 ') (H-)ft(i-y)
2 (HAa) c- 2 ~ b(i— x)
so that the quotient
ki (Salt'BAi) (AcidHA 2 ) x c 2 —b( i—x)
k 2 ~ (Salt BA 2 ) (Acid HAi) ~i—x c-^—bx
or \
(Salt BAi) k x (Free Acid HAQ |
(Salt BA 2 ) k 2 (Free Acid HA 2 ) J
represents the equation from which the distribution ratio
X
of the base - — — may be calculated for any case, as a
function of the acid dissociation constants and their
quantities (c 1 and c 2 ). The solution of this general
equation leads to the expression
(K—i)b -\-Kc\ d~c 2
± \^[(K — i )6 -H Kci + c 2 f- 4 (K ~ i )Kbc 1
* — ' < l8 >
98 THE THEORY OF ELECTROLYTIC DISSOCIATION .
and
(K—i)b — Kci—C2
i — #=-
in which
: v [(iv — i )b ~r Kc\ + C2] 2 — 4(K — i )Kbci
2 (K-i)b ’
K=
h
The simplest case, investigated by Ostwald and theo-
retically calculated by Arrhenius, was the one in which
equivalent quantities of a salt and a second acid were
mixed, or, since we may look upon the salt as made up of
one equivalent each of base and acid, it follows that in
our general equation we must write b=c 1 =c 2 . That
means that the above quotient (17) becomes
ki x b-x x 2
k 2 1 — x b(i — x) ( 1 — x ) 2
Since in the case of equal concentration the ionic
concentrations of pure (unmixed) acids are to each other
as the roots of their dissociation constants (p. 47), we may
with Arrhenius also express this equation thus, that both
acids divide themselves between the base in the same
ratio as their degrees of dissociation would be, if each
were present alone in the volume considered. Arrhenius,
derived this for the case of a strong and a weak acid.
EQUILIBRIA AMONG SEVERAL ELECTROLYTES . 99
In both cases Arrhenius compared his calculations with
Ostwald’s measurements, and found an excellent agree-
ment, as the following examples show. They refer to
solutions which contain of each of the three substances
0.33 moles per liter, resulting from the mixing of- 1 liter
of each of the three normal solutions. The figures in
the table give the value x, that is, the portion of the first
and stronger acid consumed per mole of base.
Distribution-ratio of Two Acids between One Base.
(Observed by Ostwald, 187S; Calculated by Arrhenius, 1SS9.)
Observed.
Calculated-
UNO, : CUCH.COOH
0.76
0.70
HC 1 : Cl 2 CH.COOH
0-74
0.70
CCI3COOH : CkCH.COOH
0.71
0.70
CHC 1 XOOH : CH 3 CH(OH)COOH
0.91
o -95
CCI3COOH : CHodiCOOH
0.92
0.92
CCI3COOH : HCOOH
0.97
0.96
HCOOH : CH 3 CH(OH)COOH
°-54
°-5 5
HGOOH : CH3COOH
0.76
0.77
HCOOH : Ca^COOH
0.80
o -79
HCOOH : iso-CgHyCOOH .
0.81
0.79
HCOOH : C,H 5 COOH
°-79
0.80
HCOOH : CH>OHCOOH
0.44?
0.54
CH3COOH : CgHyCOOH
o -53
0-53
CH3COOH : iso-CjHyC O OH
°'53
0-53
The more complicated case, the interaction of a weak
acid with any concentration, not equivalent, .of the
salt of another weak acid (b = ci ;> £2^ , was investigated
by Wolf 1 by means of conductivity studies, and was
found to agree splendidly with equation (18), easily
simplified for this case.
Zeitschr. physik. Chem., - 10 , 226 (1902).
loo THE THEORY OF ELECTROLYTIC DISSOCIATION.
INDICATORS.
A number of weak electrolytes possess the peculiarity
of having a very different color for the undissociated
part and its ions, or of having only one of the two colored.
If the substances possessing a different color in the
undissociated and dissociated condition are quite weak
electrolytes, they may be employed as “ indicators.”
This prerequisite makes it impossible for anything but
bases and acids to be classed here, salts being excluded,
since as a rule they are strongly dissociated.
In using indicators the purpose is to recognize whether
a solution is neutral, or whether it contains H' or OH'
ions in excess. If the indicator is (i) an acid, then
H* ions work against its dissociation, that is, make its
anions disappear, while OH' ions (by “ salt formation ”
with the same) produce its anions; if on the other hand
the indicator is (2) a base, then H* ions react with the
same to form salt, that is, produce its cathions, while OH'
ions force back its dissociation, or, in other words, trans-
fer the cathions to the undissociated substance.
It is scarcely necessary to add that, as far as the color
change is concerned, only the anions of the acid or the
cathions of the basic indicators come into question, since
neither the H’ nor the OH' ion possesses color, as is
proved by the existence of colorless acids and bases
(see p. 13).
The theory of the action of indicators may be developed
by means of the recently derived equations, if we only
remember that here also we have the competition of
two acids for one base, of which the indicator acid is
EQUILIBRIA AMONG SEVERAL ELECTROLYTES, iol
one, or the competition of two bases for one acid, of
which the indicator base is one.
An example will make the matter clear. Suppose we
desire to titrate dichloracetic acid (ki =5.1 Xio" 2 ) by
means of the indicator acid />-nitrophenol (i 2 = i.2Xio“ 7 ).
(We shall see later that in this case it would be better
to choose another indicator.) Nitrophenol is a weak
acid, which by itself in an aqueous solution is so little
dissociated that the intensely yellow color of the nitro-
phenol anion is scarcely perceptible. Upon the addition
of a base, i.e., OH' ions, it is, however, as good as com-
pletely converted into (H 2 0 and) nitrophenol salt, which
means nitrophenol anions, and so gives rise to yellow
color.
Let us assume that we are titrating 100 c.c. of a dichlor-
acetic acid solution of the concentration 2 c x (per liter),
to which a quantity of nitrophenol has been added such
as to give the latter the concentration 2 C 2 (per liter), with
an equally strong base, say potassium hydroxide, likewise
of the concentration 2C1. We now add an amount of
alkali which is exactly equivalent 1 to the dichloracetic
acid, and apply the general avidity equation (see p. 97,
equation [18]), in order to determine how much of the
alkali goes to the dichloracetic acid (acidi) and how
much to the nitrophenol (acid 2 ), since these are the two
acids competing for the base.
ki 5.1 Xio 2 .
For the above case A = y- = rr — 31=4.25 Xio~, and
ko 1. 2X10 7 D ’
also b=c x . By introducing these values into equation
1 Thereby the original concentrations 2C1 and 2 c z sink to half the
values, Ci and c 2J on account of the doubling of the volume.
102 THE THEORY OF ELECTROLYTIC DISSOCIATION.
fiSj and neglecting i as compared with K, then on the
c i
assumption that the indicator concentration =
which will be about the equivalent of the quantities prac-
tically employed, we find in round numbers for
the portion i—x, which is the portion left for the nitro-
phenol by the added base. That is, 999995 millionths
of the dichloracetic acid is neutralized by the concentra-
tion Ci of the base, and — — — falls to the concentration
ioooooo
c 2 of the nitrophenol, which we assumed to be=^^.
Hence of the nitrophenol is first neutralized, i.e.,
0.005^2 is the titer of the yellow nitrophenol anions. If
now one more drop ( = approx. 0.04 c.c.) of the titrating
alkali of the concentration 2c x is added, there is brought
into the solution 0.04 X 2C\ = 0.080^! millimole of base,
while there was still left in the approximately 200 c.c.
. _ . 200X<-Ci ,
of the titrating mixture = o.ooiCi millimole of
IOOOOOO
free dichloracetic acid. Even if straightway all the
dichloracetic acid would now be neutralized, there would
still be left 0.079^1 = 79^2 millimoles of alkali for the
neutralization of nitrophenol, of which almost all of the
2ooc 2 millimoles in the 200 cx. are still present unneu-
tralized. There will be formed, then, in our 200 cx. of
titrating liquid (outside of hydrolysis) about jgc 2 miHir
moles of nitrophenol salt, which means a titer of
7QC‘>
— -= approx. 0.04c 2 normal as to yellow nitropheiiol
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. 103
anions. With one drop of alkali less the titer = 0.005^2;
this drop then increased it about 80 times.
The calculation shows that it is of importance to
choose an indicator with a somewhat small dissociation
constant £ 2 > so that the same does not take up appreciable
quantities of the base before the stronger acid is neutral-
ized; the wreaker the acid to be titrated is, the much more
w r eak the indicator must be, since by the avidity equation
the ratio of the constants is the determining factor.
Likewise the indicator concentration must not be too
great, so that the mass action does not compensate for
the weakness; on the other hand, it is not advantageous
to take the concentration too small, so that the first drop
of excess of the titrating solution may be most effectively
utilized to form the colored indicator ions. As a rule,
then, it is best to take an amount of indicator equivalent
to the quantity of acid or base contained in one drop of
the titration liquid. This may be accomplished by
adding to the reaction mixture one drop of an indicator
solution made up equivalent to one of the titration liquids.
The selection of an indicator having a very small
dissociation constant, such as phenolphthalein, makes
it necessary that the base used in neutralization be strong.
Suppose, for example, we titrate our acid w T ith ammonia,
using phenolphthalein as indicator, then in the first stages
of the titration up nearly to the neutral point w r e wrould
have formed essentially the ammonium salt of the acid
to be neutralized, and so the first traces of excess of
ammonia would find themselves in the presence of a
large quantity of ammonium ions. These (according to
p. 71) can bring only very few OH' ions into the solution
104 THE THEORY OF ELECTRGL YTIC DISSOCIATION.
and would not be able to dissociate the indicator acid
to any marked extent, or, in other words, the ammonium
salt of the indicator becomes far-reachingly hydrolyzed,
which amounts to a non-formation of its colored ions. In
such cases, therefore, it would require a considerable
excess of ammonia to gradually form sufficient indicator
ammonium salt to show the color change distinctly, that
is, the turning-point would not be sharp. It is evident,
then, that no very weak indicator acid can be employed
in the titration of weak bases, but that we must employ
relatively strong ones (always, however, much weaker
than the acid taking part in the titration). Such rela-
tively strong indicator acids are, for instance, nitrophenol
and methyl orange. On the other hand, a very weak acid
(or a strongly basic) indicator such as phenolphthalein
is necessary in titrating weak acids, so that the indicator
in its competition with the other acid does not successfully
interfere (i.e., form anions) before the neutralization
of the latter.
From this we may derive the following rule for the
selection of the indicator acids (indicator bases are not
in use). If we have to titrate:
1. Strong acid and strong base — indicator at
random;
2. Strong acid and weak base — indicator strongest
(methyl orange, nitrophenol);
3. Weak acid and strong base — indicator weakest
(phenolphthalein, litmus) ;
4. Weak acid and weak base — to be avoided,
since the color change with every indicator
is not sharp.
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. 105
The importance of the exact knowledge of the electro-
lytic equilibria for these relations is shown by the following
question: Which indicator is to be chosen in order to
titrate hydrochloric acid, containing ammonium chloride,
with potassium hydroxide?
Having here case 1, one might think it permissible
to choose at random and employ phenolphthalein as
indicator, since it gives the sharpest color change, and
potassium hydroxide is ordinarily easily titrated with it.
In this case, however, we must remember that the NH^
ions of the ammonium chloride addition destroy the
large OH' concentration of the first excess of potassium
hydroxide by forming undissociated ammonia, and that
phenolphthalein in order to form salt (red coloration)
requires much OH'. Therefore, in order to get a sharp
end-point it is necessary to use a stronger acid indicator;
hence case 1 must be modified thus: if the solution
contains a salt with a weak cathion, then the equilibrium
relations correspond to those of case 2; if it contains a
salt with a weak anion, then they become those of case 3.
HETEROGENEOUS ELECTROLYTIC EQUILIBRIA.
It is scarcely possible to treat here exhaustively every
phase of electrolytic equilibria; for that reason let us
consider only one more case, one which is of fundamental
significance to analytical chemistry, namely, that the
concentration of an electrolyte is limited by its solubility.
As to form such equilibria become simpler, because the
concentration or active mass of the substance, which is
present in the state of saturation and is kept in this con-
IO 6 THE THEORY OF ELECTROLYTIC DISSOCIATION.
dition by the presence of the substance in the solid state,
becomes constant. We have learned to recognize the
electrolyte <£ water ” as a substance of never varying
concentration, whose ionic product, the water constant
is unchanging, because the undissociated water always
has very nearly the same concentration. Precisely the
same holds for the ionic product of any substance whose
saturation is maintained, for then, according to Nemst’s
partition law, the solution contains under all circumstances
(at constant temperature) an invariable 1 concentration l
of undissociated electrolyte. According to the law of
mass action, the product of its ions M* n and A ,m is :
(M*) n • (A') m = k
in which, according to Ostwald, L stands for cc solubility
product ” (or the ionic product). This equation show's
us at once what the effect is of the addition of an electro-
lyte having, for instance, M* in common: we have formed
immediately more undissociated substance M n A m , but
since the solution was previously saturated with the same,
it precipitates until the ion A', not in common w r ith the
addition, is reduced so far that its concentration, following
the above equation, has become
that is, upon increasing M*, A' becomes correspondingly
smaller than originally.
1 It is true the presence of other electrolytes changes somewhat the
solvent medium. Compare Arrhenius, Zeitschr. physik. Cfiem., 31,
T 97 (i899)-
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. 107
This formulation we owe to Xernst, 1 and a thorough
experimental testing to Noyes, 2 as well as to Goodwin, 3
who employed an entirely different method from that of
Noyes, namely, the measurement of concentration chains.
The quantitative agreement between theory and experi-
ment still suffers from the uncertainty with which the
ionic concentrations in strong electrolytes (seep. 12 1) are
burdened, but nevertheless the same is sufficient to show
the correctness of the law of solubility influence. The
following small table taken from Noyes’s measurements
teaches especially that the equivalent addition of the one
or the other ion has the same action on the solubility of a
binary electrolyte:
Solubility of Thallous Chloride (25°).
(Noyes, 1S9C.)
Concentration
of the
Addition.
Addition*
TlNOj
Addition:
HC1
0
0.0161
0.0283
0.0560
O.147
0 . 0083
0.0057
0.0033
0 . 00S4
0.00565
0.0032
With very insoluble salts, such as AgCl, the quantity
in solution may be looked upon as very nearly completely
dissociated, on account of its great dilution, so that only
1 Zeitschr. phvsik. Chem., 4 . 372 (18S9).
2 Ibid-, 6, 241 (1S90).
* Ibid.* 13 ,. 588 (1894k
xoS THE THEORY OF ELECTROLYTIC DISSOCIATION.
a minimum portion of the quantity dissolved is undis-
sociated substance, while the major portion is present
as ions. If, for example, we reduce to to the Ag* ion con-
centration of a saturated AgCl solution by the addition
of HC1 (i.e., CF), it is practically equivalent to reducing
the total amount of silver (Ag* ions+undissoc. AgCl)
present in the solution to to, even, if strictly speaking, the
quantity of the undissociated AgCl is not changed at all
in its concentration by the addition.
Let us now consider conversely a mixture of two
electrolytes, each of which contains an ion of a difficultly
soluble substance, for example AgN0 3 and KC1, and
discuss the conditions, when and how much of the diffi-
cultly soluble substance is formed. In any case the
quantity of undissociated AgCl becomes
k • (AgCl) = (Ag*)(CF).
If either the Ag* or CF ions or even both ions are very
dilute, so that the concentration (AgCl) formed from
these may be smaller than that required for saturation,
then no precipitate of AgCl is produced, for not until we
have (Ag*)(CF)>Z can solid AgCl separate; from there
on, however, an increase of either the one or the other
kind of ion no longer produces an increase of the ionic
product, since the value L is its maximum value. If
both ions are present in equal quantity, then
fAg') = (CF)=\/L, the solubility of the silver chloride in
water (more exactly, after subtracting the undissociated
AgCl). The value of this solubility product L , which
of course varies for different substances, is of fundamental
EQUILIBRIA AMONG SEVERAL ELECTROLYTES . 109
significance in the formation and conversion of pre-
cipitates. 1 Several examples will show this.
If AgCl reacts with KI, Agl and KC1 are formed.
How far does this reaction go? In the common solution
of the four substances the Ag* , Cl' equilibrium demands
(Ag-) =
^AgCl
(CIO ’
and the Ag' , V equilibrium,
hence we have
(Ag*)= :
(10 5
Z Ag q_(C10_
La s i (10
That is, the interaction proceeds until the ratio of the
(CIO • (10 ions has reached the constant value K, the
quotient of the two solubility products. If therefore we
use for the precipitation of any Ag' solution a potassium
chloride and iodide mixture in the ratio (Cl') : (I') =
i A g ci ; ^Agi, then the difficultly soluble salts also
precipitate in this ratio until the remaining Ag' con-
centration satisfies both solubility products. If we
further add KI to this equilibrium, this would disturb the
equilibrium ratio (Cl') : (I'), and consequently the reaction
AgCl+I' = AgI + Cl' takes place, until the old value
(Cl') :(I') is attained; but also the reverse, the addition of
KC1 converts some Agl into AgCl with the production
See in particular Findlay , Zeitsciir. physik. Chem., 34 , 415 (1900).
no THE THEORY CF ELECTROLYTIC DISSOCIATION .
of I'. This latter change, however, will have to take
place to only a very slight extent in order to raise the I'
concentration to the value of the equilibrium, since i A gi
is very much smaller than L^c \ ; according to Goodwin, 1
the latter is 1.56 Xio“ 10 and the former 0.94 Xio~ 16 , so
that the concentration ratio of the Equilibrium (Cl') : (I')
must be equal to 1600000. From this it follows that
even with the greatest concentrations of potassium
chloride, practically speaking, no appreciable quantities
of potassium iodide are left, but are as good as entirely
consumed in the conversion of AgCl into Agl. 2
An exactly analogous case occurring in analytical
chemistry is Mohr’s method for chlorine titration by
means of silver solution with chromate addition. Silver
chromate as well as chloride is difficultly soluble; how-
ever, the latter much more so than the former, so that the
equilibrium ratio of the concentrations (Cr 0 4 ") : (Cl')
is very large. As long, then, as we have present in the
solution to be titrated much Cl' as compared with the
small amount of Cr 0 4 " (serving as indicator), essentially
only AgCl can precipitate upon the addition of Ag* ions.
Finally, when so much Cl' has thereby been removed
from solution (practically speaking, all) that -the chromate
ions can take part in the precipitation, the deep-brown
silver chromate is formed alongside the white chloride.
Conversely, in any solution containing an appreciable
concentration of chloride, the brown precipitate of
1 1. c.
2 In case the precipitates form solid solutions with one another, the
relations .are -changed; -compare F. W. Kuster and Thiel, ^eitgchr,
anorg. Ch^m-i. 19 , .81;. 23 , 25,. 24 , . 33 v 129 (1.899-1903)..
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. :n
Ag2Cr0 4 is completely converted into AgCI and soluble
chromate, a fact employed in sounding ocean depths by
means of a patent sounding instrument. In this, glass
tubes are used closed at one end and lined on the inside
with silver chromate; these, are lowered into the ocean.
As high as the sea-water enters the tube, corresponding
to the pressure of the depth, the silver chromate is con-
verted into white chloride, and the brown-white line of
demarcation between the two permits the calculation of
the compression to which the air within the tube was
subjected at the greatest depth.
If we have two salts of the same metal, approximately
equal as to insolubility, in equilibrium with a solution, then
under all conditions we must also have in the solution an
approximately equal concentration of the precipitating
anions, or if they are not equal such equality must be
brought about by one precipitate being changed into the
other.
For example, if we have silver chloride present in a
solution of silver nitrate, and precipitate the silver ions of
the nitrate with the aid of KCNS, we obtain AgCNS as a
second' precipitate. So long as the precipitation of the
silver is not complete, the solution will not be capable of
containing sulphocyanate anions; as soon, however, as the
first excess of sulphocyanate ions is added the equilibrium
with the AgCI is disturbed, because suddenly the ratio
(CNS') : (Cl') in the solution is shifted very much in
favor of CNS'. The equilibrium then adjusts itself in
such a way that the excess of CNS' ions reacts with AgCI
to form AgCNS and ’ Cl' ions- until the necessary
(Cl') : (CNS') concentration ratio is re-established.. The
H2 THE THEORY OF ELECTROLYTIC DISSOCIATION .
result Is that a sulphocyanate excess is not shown at once
by the ferric indicator reaction, and in order to attain
this, that is, prevent the reaction of the sulphocyanate
with the AgCl, it is necessary in the Volhard chlorine
titration method to remove the AgCl by filtration before
the addition of sulphocyanate.
The greater the solubility product or the solubility of
a precipitate is, the greater — for a given concentration of
one of its ions — the other ion, contained in the u pre-
cipitating agent,” must become before separation of the
precipitate sets in.
The extreme of insolubility is probably that of the
sulphides, which require as precipitating ions the sulphur
ions S". These S" ions are contained in greatest con-
centration in the alkali sulphides, somewhat less in
ammonium sulphide on account of hydrolysis, very much
less in hydrogen sulphide, which, according to Walker, 1
splits up to a just measurable extent into the ions H' and
HS'. A o. i - NH 2 S solution, which is one almost saturated
with H 2 S at a pressure of i atm., contains only 0.000075 2
mole HS' ions per liter; these in turn are further dis-
sociated to an extremely limited extent according to the
equation HS'=H‘-fS". Hence the concentration of the
S" ions in an H 2 S solution is exceedingly small and is
made still smaller by the addition of acid, whose H* ions
force down the HS' ions to concentration magnitudes of
about io~~ 9 . In spite of this, the inconceivably small
S" concentrations resulting are sufficient to enable a
1 Zeitschr. physik. Chem., 32 , 137 (1900); Joum. Chem. Soc., 77 , 5
2 -V^TyXicr 4 *:©.! (see p. 55).
EQUILIBRIA AMONG SEVERAL ELECTROLYTES 113
whole series of metals to so easily reach their solubility
products that they are precipitated even from their most
dilute solutions.
It is plain to see now why we group qualitative
analysis according to these sulphide solubilities, for:
i- The most insoluble sulphides are formed even with
the few S" ions of a strongly acid hydrogen sulphide
solution, that is, they do not dissolve in acids (Pb, Ag, Hg,
Cu, Bi, As, Pt, Au). In other words, they send so few
S" ions into solution that even with the high H' concen-
tration of strong acids no H 2 S is produced.
2. The very insoluble sulphides (Cd, Sn, Sb) are partly
but not completely precipitated from a strongly acid
solution, i.e., very small metal ion concentrations no
longer give a precipitate with the extremely small S"
concentration, or the sulphides are dissolved (form
H 2 S) by concentrated acids.
3. The appreciably soluble sulphides (Zn, Co, Ni)
precipitate only from neutral or H 2 S solutions acidified
with a weak acid, but usually not completely until the
H* concentration of the liberated acid is reduced by
means of sodium acetate, for example (see p. 71), thereby
increasing the HS' and S" concentrations.
4. The markedly soluble sulphides (Mn, Fe) require for
their precipitation high S" concentration, which is only
attainable in alkaline solution, i.e., a solution poor in H*
(ammonium sulphide, sodium sulphide). Even weak
acids such as acetic acid possess sufficient H' ions to form
H 2 S with the S" ion of the aqueous solution of Mn or Fe
sulphide — in other words, to dissolve the sulphide.
Of interest is also the behaviof of difficultly soluble
1 14 THE THEORY OF ELECTROLYTIC DISSOCIATION
oxides and hydroxides, which, in so far as they are soluble
in water, produce in addition to the particular cathion the
anions O" and OH' respectively. On account of the
presence of water the equilibrium condition, (H*) 2 * (O") =
k and (H*j* (OH'j = £- a , respectively (see p. 55), must
always be fulfilled. This equilibrium constant is ex-
tremely small, so the H‘ concentrations of the weakest
acids are in most cases sufficient to dissolve, with the
formation of H 2 0 , these difficultly soluble substances.
Therefore only the most insoluble oxides (and hydroxides)
are not dissolved in acids to an approximately quantitative
extent, especially when the acid is at the same time a
weak one.
A case of this was found .by Jaeger 1 in dissolving HgO
in H 2 F 2 - Here he found the ratio of the free acid remain-
ing in the solution equilibrium to be (H 2 F 2 ) :(HgF 2 ) = 3.6
as a mean. It is easy to see that this equilibrium is
nothing more than a hydrolytic one, which is only dis-
tinguished from the former instances in that the base
HgO liberated by the action of H 2 0 on the salt HgF 2
attains its saturation concentration and therefore enters
equation (15) (p. 90) with constant active mass
= Hydrolytic Constant
(bait) (HgF 2 )
so that, as found, (H 2 F 2 ) : (HgF 2 ) has a constant value
( 3 - 6 ) 2
1 Zeitschr. anorg. Chem., 27 , 26 (1901).
3 From which by (15), knowing the solubiiiiy 01 Jtigu, tne dissociation
constant of HgF^ould be calculated.
EQUILIBRIA AMONG SEVERAL ELECTROLYTES . Ii5
The solution of a precipitate is usually based upon the
fact that one ion of the substance added unites with one
ion of the difficultly soluble substance to form an undis-
sociated body, and thereby disturbs the solubility product
of the original precipitate. For instance, if we have a
suspension of BaC0 3 in water, there are present dissolved
in the water sufficient Ba* * and C0 3 " ions so that we have
(Ba-):(C 0 3 ")=iBa C03 -
An addition of acid, H* ions, forms undissociated car-
bonic acid with the weak CO 3" ions, whereby the CO3"
concentration is reduced and a corresponding amount
of the dissolved undissociated BaC0 3 is ionized; then,
however, the undissociated part ceases to be saturated,
and consequently more solid BaC0 3 passes into solution.
In general in the same way every precipitate not too
insoluble and containing the anion of a very weak acid
(carbonates, sulphides, cyanides, phosphates, oxalates, etc.,
and especially hydroxides) must be dissolved by H' ions
(acids), in that the anions are consumed in the production
of the undissociated weak acids, among which water is to
be counted.
Analogously the solvent action of ammonia and its
derivatives upon the precipitates of many heavy metals is
explained. The metal ions in these cases are to a very
great extent taken up by the amines to form complex
“ amine ” ions, and are thereby removed from participa-
tion in the solubility product, which in turn strives to
re-establish itself at the expense of the undissociated
portion of the dissolved solid, resulting in a solution of
the precipitate.
tl6 THE THEORY OF ELECTROLYTIC DISSOCIATION .
Complex-forming ions, such as cyanogen and iodine
ions, have a somewhat different kind of solvent action on
cyanides (Cu, Ag, Cd, Ni, etc.) and iodides (Pb, Hg n , Ag),
because they take up the undissociated portions of these
as a “ neutral part ,” 1 * so that the solid must pass into
solution in order to keep up the concentration of satura-
tion.
Special attention has been attracted to several cases,
more in the nature of curiosities, in which, by the inter-
action of a difficultly soluble (heavy metal) oxide and
a neutral salt, alkaline reaction appears, i.e., OH' ions
are formed. This, for example, takes place between
HgO and Ell. The dissociation theory also explains this
phenomenon very simply. Let us consider the oxide
ion equilibrium, which, since oxides are formed from
metal M* and OH' ions, may be formulated thus:
(M-)(OH')=L 0 >
in which Lq represents the solubility product of the oxide.
Accordingly, every electrolyte, which consumes the
cathions M* either for the formation of a difficultly
soluble compound (as Agl) or for a complex formation
(as Hgl 4 ", Ag(CN) 2 ', Pbl 3 ', BF 4 '), must bring about an
increase of the OH' concentration, that is, an alkaline
reaction.
So among others the following cases may be predicted,
and are confirmed experimentally . 3
1 See Abegg and Bodlander, Zeitschr. anorg. Chem., 20 , 471 (1899).
3 Heinrich Biltz, in his “ Experimentelle Einfuhrung in die anorgan-
ische Chemie” (Kiel, 1898), p. 86, maintains that HgO + 2KCN is
EQUILIBRIA AMONG SEVERAL ELECTROLYTES, n?
Appearance of Basic Reaction by Interaction of Neutral
Compounds.
(Bersch, 1S91 [Ostwald’s Zeitschr., S, 383]; Abegg, 1903.)
Oxide.
Neutral Salt.
Reaction Product.
PbO
Potassium
iodide
Pbl„
C (
bromide
PbBr 0
Fe(OH),
1 c
i C
fluoride
FeF 3 (undissoc.) (L)
1 1
oxalate
Fe(C 2 0 4 ) 3 "' (complex) (L)
Cu(OH) :
t <
1 1
tartrate
Fehling ion (complex) (L) ‘
tt
sulphocyanate
Cu-sulphocyanate complex (L)
< <
1 1
thiosulphate
Cu -thiosulphate complex (ZA
Ag 2 0
t i
i t
iodide
Agl
i £
bromide
AgBr
1 1
£ £
chloride
AgCl
1 1
£ £
thiosulphate
Ag-thiosulphate complex (L)
HgO
£ £
iodide
Hgl 4 " complex ( L )
£ £
£ C
bromide
HgBr/' complex (L)
it
£ £
chloride
HgCl 4 " complex (L)
£ £
£ £
oxalate
Hg-oxalate complex (L)
£ (
£ £
thiosulphate
Hg-thiosulphate complex
Cd(OH).
« t
£ c
£ £
£ £
£ £
iodide
bromide
chloride
1 inner complex, very
fSSti little dissoc. (L)
BF 4 ' complex (L)
B(OH) 3
£ £
fluoride
All these reaction products, of course, do not react with
alkalis to separate metal hydroxides.
A reverse curiosity, the appearance of an acid reaction
upon the mixing of neutral AgNOg with alkaline
Na 2 HP0 4 , is explained in an exactly analogous way by
probably the only reaction of the kind. However, the above con-
federations of the case, based on the ionic theory, give, as we see, numerous
reactions. The still more numerous cases in which KCN as a result of
complex formation brings about alkaline reaction are purposely omitted,
since, on account of the alkaline reaction of the KCN to begin with, they
are not as striking as the above produced with absolutely neutral salts.
In the cases marked (L) in the table, solution of the oxide occurs; in
the others, conversion into a more difficultly soluble salt-
US THE THEORY OF ELECTROLYTIC DISSOCIATION.
the ionic theory. The latter salt contains the ions Na'
and HP0 4 ", and this anion dissociates with the separation
of H" ions, according to the equation
HPO 4 " «=> H' -f P0 4 '".
This dissociation is, however, exceedingly slight as long
as appreciable amounts of OH' ions are present, owing
to the hydrolysis of the Na 2 HP0 4 , which is due to the
weakness of the anion. Since by the previous equation
and the law of mass action
, (HPO/Q
(PO 4 "0 ’
the concentration of the H' ions grows with diminishing
P0 4 '" ions, and the Ag* ions remove these PO/" ions by
precipitating Ag 3 P0 4 , so accordingly the addition of
AgN0 3 must produce acid reaction.
As for the rest, the appearance of alkaline reaction is
absolutely analogous to the appearance of acid reaction
when we use a neutral salt such as CuS0 4 , HgCl 2 , or
AgN0 3 to remove by means of its cathion (through
producing insoluble sulphide) the S" ions from H 2 S and
so force the hydrogen of the same to become ionic. This
is usually described as decomposition of the salt and
liberation of its acid by H 2 S. In place of H 2 S, of course
any weak acid will serve which gives difficultly soluble
metal compounds, i.e., such whose saturated solutions
contain very few metal ions. The previously discussed
case of Na 2 HP0 4 is therefore only a special case of this
general manifestation.
The salts of very insoluble hydroxides, such as those
EQUILIBRIA . AMONG SEVERAL ELECTROLYTES. 1*9
of Al"’, Cr”', and Fe*", also give an acid reaction with
the neutral water, because their cathions consume the OFF
of the latter — a phenomenon that we have already learned
to recognize as hydrolysis.
The common feature of all these reactions is that the
metals and the acid anions combined with OH' and H*
respectively are contained in considerably smaller
concentration in the compounds produced (precipitate,
complex, or undissociated substance).
Heterogeneous equilibria may also appear in conjunction
with hydrolysis, as shown by the action of water on tin,
plumbic, bismuth, antimony, and the strongly dissociated
mercurous and mercuric salts (nitrate and chlorate).
Here the OH' ions of the water combine with the very
weak cathions to form difficultly soluble basic salts, which
precipitate as soon as hydrolysis has produced such
quantities of them that they exceed the concentration of
saturation. As a matter of course, acid reaction (H* ions)
appears here also and places a limit upon the hydrolysis.
The hydrolyzing OH' ions may by the addition of acid
be so reduced at the very outset that no appreciable hydrol-
ysis and hence no precipitation of basic salt takes place.
This fact is likewise made use of in analytical chemistry.
Just as precipitating reactions, and through them the
heterogeneous equilibria, play a leading part in analytical
chemistry, so the knowledge of the numerical values
of the solubility products L 8 for the various precipitates
is of primary importance. A series of determinations
of this kind have been made by Goodwin , 1 Immerwahr , 2
1 Zeitschr. physik. Chem., 13 , 641 (1S94).
2 Zeitschr. f. Elektrochem., 7 , 477 (1901).
120 THE THEORY OF ELECTROLYTIC DISSOCIATION.
Noyes , 1 Kohlrausch and Rose , 2 Bodlander , 3 Sherrill , 4
v. Ende , 5 Kiister and Thiel, and others , 6 and the following
figures are taken from these :
Saturation Concentrations and Solubility Products of
Difficultly Soluble Salts.
Ag.O
Ag- -1.5 Xro- 4
l 8 = - —
AglO,
“ =x-9 Xio~*
44 =3.6 Xio' 8
AgCl
“ =1 .25X io~ 5
“ = 1.56X10-° (25°)
AgSCN*
44 =1.1 Xio~ 8
“ =1.2 Xio- 13
AgBr
44 =6.6 Xio -7
“ =4*35X IO “ t3 (25°)
Agl
44 =1.0 Xio- 16 * 4
Ag 2 Cr 0 4
14 = 1.7 Xxo- 4
“ =1.0 Xio- 11 (iS c )
TICi
44 = 2 . 65 X IO— 4 (25°)
TIBr
44 =2.0 XlO“ 3
44 =4.0 Xio* 8
TIBr
“ =8.7 Xio- 3
44 =7.6 X io~ 5 (68-5° j
TISCN .......
44 =1.5 Xro~ 2
44 = 2 . 25 X 10 4 (25°)
tlso 4 .......
44 =9.0 Xic~ 2
44 =3-6 Xio~ 4
CuCi
.. .. Cu* =1.1 Xio -3
“ =1.2 xio-°
CuBr
“ =2.0 Xio- 4
“ =415x10-*
Cul
“ =2. 25X10-'
“ =5.1 Xio- 13
HgjClj
“ = 3-5 Xio- ,s (25 c )
HgJJi-j
' 44 =7-0 Xic -8
“ =1-3 Xio -21
Hg,J„
“ =3.0 Xio- 10
“ =1.2 Xio -3 ’
Hg^o 4
44 =8.^ Xio- 4
“ =3.0 Xio— 0
HgCI,
“ =2.6 Xio- 15
HgBr,
■ 44 =2.7 Xio~ 7
“ =8.0 Xio- 30
Hgl 2
...... “ =2.0 Xio- 10
“ =3-2 Xio- 3 *
PbCIj
Pb” =2.0 X io~ 2
44 =1.0 Xio -4
PbBr 2
44 =2.0 Xio -2
44 =6.0 Xio- 8
Pbl 2
“ =i.S Xio- 3
44 =1.0 Xio -7
PbSO. t
..... 44 =1.5 Xio- 4
44 =2.2 Xio -8
1 Zeitschr. physik. Chem., 6, 241 (1890); 42 , 336 (1903).
2 Ibid., 12 , 241 (1893^
3 Zeitschr. anorg. Chem., 31 , 474 (1902).
4 Zeitschr. physik. Chem., 43 , 705 (1903).
5 Zeitschr. anorg. Chem., 26 , 129 (1901).
8 Ibid., 24 , 57 (1900), and 33 , 129 (1903); see also Wilsmore, Zeitschr.
physik. Chem., 35 , 305 (1900).
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. 121
ANOMALY OF STRONG ELECTROLYTES.
While in the preceding discussions it is safe to say the
law of mass action, as applied to an extended series of
reactions between ions and undissociated substances,
found its excellent verification, yet it seems in one es-
pecially simple and important case to utterly fail, namely,
in the dissociation of the so-called strong electrolytes —
the salts — and the strong acids and bases. Whether we
derive the degree of dissociation of these electrolytes from
the conductivity
or from the freezing-point
, we arrive at values for the expression
C£ 2 ‘C
of
i —a
the law of mass action which for the different concentra-
tions c decidedly deviate from the demanded constant,
and therewith prove that, for some reason, either the law
of mass action is to be modified for these electrolytes, or
the methods for the determination of the degree of dis-
sociation a in these cases give incorrect values.
Recently this vulnerable spot of the dissociation theory
has been very assiduously investigated and discussed, and
we are indebted to Jahn in particular for a series of
brilliant measurements of precision. He attempted to
get at the degree of dissociation by a third method, namely,
that of the measurement of concentration chains. Up
to this time this method had hardly been used, because
of its lack of sensitiveness for purposes of ordinary
accuracy.
It would take us too far to give here the theoretical
considerations which rest on the exact application of
122 THE THEORY OF ELECTROLYTIC DISSOCIATION.
thermodynamics, especially as up to the present we can
by no means look upon the problem as solved. There
is a tendency on the one hand to assume that in the
solutions of strong electrolytes the ratio of the equivalent
conductivities for different concentrations cannot give the
degree of dissociation accurately, because, in consequence
of the variable friction, the mobility of the ions varies in
the solutions according to the amount of salt contained
and cannot be assumed as equal. On the other hand,
the osmotic methods (depression of the freezing-point,
etc.) might fail, for reasons which may be of a physical
as well as of a chemical nature.
Nemst and Jahn 1 find the physical reasons in that
there exists in the solution an interaction between the ions
and the undissociated molecules, which counteracts their
mutual independence and so causes the osmotic pressure
to be different from that which, according to van’t Hoff’s
law r , corresponds to the concentration.
From the fact that the osmotic laws hold for non-
electrolytes and weak electrolytes, Jahn draws the con-
clusion that such an interaction between the undissociated
molecules may be neglected. He further makes it
plausible that the ions have no marked influence on each
other, since the electrostatic attractions of the unlike-
charged are just counteracted by the repulsions of the
like-charged; that is, there 'would be left only the inter-
action of the undissociated molecules with the ions, which
would have to be considered accountable for the devia-
1 Zeitschr. physik. Chem., 33 , 545, 35 , 1; 37 , 490; 38 , 487; 41 , 257
Q1900-1902).
EQUILIBRIA AMONG SEVERAL ELECTROLYTES . 123
tion of the osmotic pressure from vairt Hoff’s law. The
mathematical form in which this is to take place has been
shown in the latest investigation of Jahn, just referred to.
The result is that the dissociation constant is not given
by the formula
9 9 0(211— N)
n z n- —
= £, but should be expressed by e K ° =k,
N—n r J N —n ’
in which N is the total molecular concentration, n the
ionic concentration, no the molecular concentration of the
solvent, e the base of natural logarithms, and a the
characteristic constant of the interaction named.
That this formula agrees well with the freezing-point
determinations is shown by the following calculation of
Jahn, using Abegg’s freezing-point determinations on
KC1 with the selection of a suitable a value:
N . . 0.0237 0.0354 0.0469 0.0583 0.0697
n c.0208 0.0302 0.0384 0.0463 0.0525
2 a( an—N)
— e n ° ..0.132 0.147 0-141 0.141 0.125 Mean: 0.137
The applicability of Jahn’s equation only shown, how-
ever, as Jahn himself states, that the physical explanation
is correct as to formulation. Indeed, it seems to us that
a number of considerations demand another interpreta-
tion of these complicated relations. The physical point
of view should lead to the conclusion that the interaction*
between ions and molecules should manifest itself with all
strongly dissociated electrolytes; at least, it would not be
dear why this influence should assume markedly different
values for substances of a similar degree of dissociation.
124 THE THEORY OF ELECTROLYTIC DISSOCIATION.
But after all among Ostwald s 1 extended material there
are to be found a number of strongly dissociated acids,
such as dichloracctic acid, maleic acid, cyanacetic acid,
and various bromine-substituted amidobenzene-sulphonic
acids, for which Ostwald' s simple dilution law, even up to
degrees of dissociation as high as 98%, gives good con-
stants. The following summarization contains some
figures pertaining thereto; under 100a we have the
degrees of dissociation in percentages up to those for
which the dissociation constant k holds, and under v the
dilutions for which the value 100a: holds:
Strong Electrolytes which Obey the Dilution Law.
TO ? k
JO 0 a
V
CL»-acetic acid
5-14
93-4
256
CN-acetic acid
0.37
>82.1
1024
Maleic acid
1. 17
92.8
1024
<?-NHo-benzene-sulphonic acid
<=>■33
>80
1024
(1:2:5) Br-NH 2 -benzene-sulphonic acid. .
1.67
97
1652
(1:2:415) Br 2 -NH 2 -benzene-sulphonic acic
7-9
97.8
556
(1:3:4: 5) Br 2 -NH 2 -benzene-sulphonic acid
2 -5
96
115°
Again, other acids show the behavior characteristic of
strong electrolytes in spite of great analogy in composition.
In any case, according to this, it is not very likely that the
high degree of dissociation essentially determines the
deviation from the law of mass action, and certainly in
the cases of the above-tabulated acids, at least, the con-
ductivity is to be looked upon as a correct measure of
the degree of dissociation.
1 1. c.; see p. 29.
EQUILIBRIA AMONG SEVERAL ELECTROLYTES . 125
Further, the physical assumption of Jahn still owes us
an explanation as to whether or not the interaction which
exists between many ions and few molecules (strongly
dissociated substances) is not likewise observable between
many molecules and few ions (weak electrolytes), as
every analogy would lead us to expect.
The chemical facts which come into consideration for
an explanation of the anomaly are on the one hand the
formation of inner complexes, and on the other the
hydration of the ions.
The formation of inner complexes was discovered by
Hittorf 1 on cadmium salts in their transference behavior
during electrolysis, and since then has been accepted
as the explanation for the variability of the transference
number with the dilution. It consists in an addition of
the undissociated molecules to one of the ions of the
electrolyte, and the extent to which it takes place depends
on the concentration of the two components of the complex
(ion and undissociated part). A quantitative investiga-
tion of inner-complex formation has not been possible
thus far, but in addition to the investigations of Hittorf,
those of Bredig , 2 Noyes , 3 and especially those of Steele 4
should be mentioned, which have experimentally placed
the fact beyond doubt. Of these, Steele especially
discusses in detail the necessity of this assumption of
Hittorf.
1 Pogg. Ann., 106 , 385 and 546 (1859).
2 Zeitschr. physik. Chem., 13 , 262 (1894).
*Ibid., 36 , 63 (1901).
4 Ibid., 40 , 722 (1902).
226 the theory of electrolytic dissociation.
That inner-complex formation is present even in the
salts of very positive metals is made highly probable by the
existence of such double salts as K 3 Na(S04)2 (glaserite),
KMgCl 3 (camallite), etc. We shall therefore have to
take into consideration, even in the case of salts such as
NaCl, etc., the possibility of an ionic formation such as,
say, Na* and NaC^'- With salts of metals of less electro-
affinity, ionic formations of that kind are beyond doubt,
as was experimentally demonstrated in every direction
for C0CI2, CuCl 2 , ZnCl2, etc., in the nice research of
Dorman, Bassett, and Fox . 1
It is well also to call attention to the fact that in the
exact equation as developed by Jahn 2 for the electromotive
force of concentration chains there is, in addition to the
logarithmic factor with the ratio of the ionic concentra-
tions, another factor proportional to the difference of the
ionic concentrations. Such a factor would have to be
present in case of the existence of ionic hydrates in order
to give due consideration to the water combined with the
ions 3 in the work of their transport from one concen-
tration to the other.
The formation of inner complexes would reduce the
concentration of the independent molecules so that the
osmotic methods (freezing-point, etc.) would give smaller
i values, as well as smaller a values, than demanded by
1 Trans. Chem. Soc., 81 , 944 (1902).
2 Zeitschr. physik- Chem., 41 , 276 (1902).
3 Compare Dolezalek, Theorie des Bleiakkumulators, p. 35 (Halle.
igoi); also translation. Theory of the Lead Accumulator, p. 65 (Wiley
& Sons, 1904); and F. Haber, Zeitschr. physik. Chem., 41 399 (1902).
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. 127
the law of mass action; accordingly, the dissociation
constants, as calculated by means of the freezing-points,
should diminish with increasing concentration. This
agrees, for example, with the experience 1 on RbN 0 3 ,
though usually one observes in the constant thus calcu-
lated decidedly the reverse course.
Just as with their own undissociated molecules, the
ions also form complexes with the solvent (hydrates),
whose existence is likewise supported by extended ex-
perimental evidence. 2 Such a formation of hydrates,
in distinction from the formation of inner complexes,
would leave the number of moles of the dissolved electrolyte
unchanged, while that of the solvent would be diminished,
and so with increasing concentration one w r ould reach
an accelerated increase of the molecular concentration
ratio, electrolyte : water, which agrees qualitatively w ith
the course of the dissociation constants calculated from
the freezing-points. 3 Even if the quantitative foundation
for this explanation is wanting, it is still noteworthy and
seems to speak in favor of the chemical explanation that
csesium nitrate, a salt of whose ions, according to a theory
of Abegg and Bodlander (see later on p. 161), one is led
to expect a minimum tendency to form complexes and
hydrates, gives degrees of dissociation according to its
freezing-point depressions,, as determined by W. Biltz, 4
which are entirely in accord with the law of mass action,
as the following table shows :
1 W. Biltz, Zeitschr. physik. Chem., 40 , 217 (1902).
2 For literature, see Biltz, 1 . c., p. 214.
3 For examples, see Jahn, 1 . c.
4 1, c.j p. 218,
128 THE THEORY OF ELECTROLYTIC DISSOCIATION.
Ci£3lU:.I XlTSATE.
J
j
c
1 X . 85c
(
i-«)
0.00766
0.0194
0.0465
0.098S
0.142
0.210
O.299
O.386
0.434
3.66
3.6 1
3-53
3-35
3 - 2 4
3 - r 5
3-°37
2.914
2.92
1.98
i -95
1. 91
1. 81
i -75 !
1 . 704
1.64
i -575
1-578
0.9S
°-95
0.91
0.81
°- 75
0.704
0.64
0 - 5 75
0.57S
c- 33 "
o -35
0.41
0-34
0.32
o -35
c -34
c - 3 °
0.34.
- Mean: 0.34
Since the degrees of dissociation taken from the con-
ductivity (^ a== 2 ~J °f caesium nitrate by W. Biltz and Jul.
Meyer gave markedly greater values than the above and
a?c
also led to no constant for ;__ a y ^ P^i 11 to see that
the conductivity in the case of this and no doubt many
other salts is not a correct measure of the dissociation,
while before (see p. 124), in regard to a number of acids
of moderate strength, we were forced to the opposite con-
clusion.
With the anomalous strong electrolytes it seems that the
conductivity in almost every instance gives the semblance
of too high degrees of dissociation. Thus, for example,
according to Biltz and Meyer, CsN 0 3 gives
for c =0-25 0.125^
Freezing-point a = 0.67 0.78
Conductivity a = 0.76 _ 0.82
EQUILIBRIA AMONG SEVERAL ELECTROLYTES. 129
that is, with growing concentration we have a very marked
increase in the discrepancy. This may, as Jahn assumes,
be due to a decreasing ionic friction in the more con-
centrated solutions; however, several conclusions follow-
ing from this are not, as tested by Sackur , 1 borne out
by experiment.
We see, then, that this material still demands extended
and searching investigation, but so much at least it seems
we may say at present with reasonable certainty, that the
law of mass action will prove itself, as usual, to hold
absolutely also for strong electrolytes, as soon as we come
into possession of perfect methods for obtaining the real
ionic concentrations or degrees of dissociation.
As to strong electrolytes we must console ourselves,
in so far as a complete molecular theoretical explanation
is concerned, with the hope of a possibly near future;
however, let us in addition mention several attempts to
express the course of their conductivities in a mathemat-
ical formula. Rudolphi 2 was the first to give an equation
for this, which was later transformed by van’t Hoff and
Kohlrausch 3 into
(1 — a ) 2
in which, as hitherto, a = -j-. The physical significance
of this formula is:
(Ionic concentration) 3 ^* (Undissoc.) 2 .
1 Zeitschr. f. Elektrochem., 7 , 475 (1901).
3 Zdtschr. physik. Chem., 17 , 385 (1895).
•Ibid., 18 , 301, 662 (1895).
130 THE THEORY OF ELECTROLYTIC DISSOCIATION .
In order to give an idea of the extent to which this equation
conforms to the observations, the following small table
may be offered:
Constants of van’t Hoff’s Dilution Law for Strong Binary
Electrolytes.
(van’t Hoff, 1S95.)
V
! kno 3 !
| (is°) :
MgS 0 4
( 18 0 )
HC 1
(18°)
KC 1
(99- 4 °)
KCl
(18°)
NaCl
(18°)
KBr
(18 0 )
V
LiCl
(18 0 )
2 i
1.63
—
4.41
1.83
2.49
1.87
2.44
2
1.27
4
1.67
0. 162
4.87
1 -79
2.2 3
I. 71
2-55
IO
1. 16
8
1.68
0.156
4-43
1.76
2.1
1.6
2.28
. 20
1.07
16
1 . 72
0.151
4.72
1.92
I -94
i -4
2. 3 S
33-3
1.02
3 2
1.82
0. 151
5- 2 9
i -9
1.87
i -43
2.4I
100
0.92
64
i
i.SS
1 0.158
1.78
1.72
1.38
2 . 72
For the sake of completeness we must mention an in-
vestigation by Storch, 1 who assumed that the dilution law
is represented by a formula in which any power of the
ionic concentration is written proportional to any other
power of the concentration of the undissociated portion.
In the formula of van’t Hoff the ratio of these powers is
3:2, that is, equal to 1.5. Storch found by extended
calculations that the power ratios, which are reproduced
as nearly as possible in the conductivity observations, are
somewhat different for the different electrolytes, KC 1 , KI ,
KOH, KNO s , HC 1 , HN0 3 , MgS0 4 , CuS0 4 , H 2 S0 4 , :
K 2 S0 4 , BaCl 2 , ZnCl 2 , varying, however, only between
1.40 and 1.577, so that in any case they approach very
closely the value 1.5 'of* the van’t Hoff formula. The
close agreement with observed values makes it possible
1 Zeitschr. physik. Chem., 19 , 13 (1896),
EQUILIBRIA AMONG SEVERAL ELECTROLYTES . 131
to foresee that the formula, 1 for the present purely em-
pirical, will some day give an interesting relationship
A
between the real degree of dissociation and the -7- values.
A 0
Before dismissing the question of the variability of the
degree of dissociation with the concentration, it is neces-
sary to inform ourselves as to the concentrations up to
which the equation of the law of mass action or the so-
called dissociation isotherm does hold. We may say, a
priori, that it cannot hold without limits, for if we
Continuously increase the concentration of the electrolyte,
in the first place we depart from the field of Cl ideal
dilute ” solutions, in which alone the van’t Hoff laws
for the osmotic pressure hold strictly, and secondly, the
replacing of the solvent by dissolved electrolyte alters
more and more the medium in which the equilibrium has
to establish itself. We can no more expect of this reaction
than of any other that it be independent of the nature of
the solvent.. The same conclusion follows from the
consideration that in so far as we are dealing with dis-
solved electrolytic liquids for the limiting case of highest
concentration, i.e., water- free electrolytes, the concentra-
tion of the ions must be extremely small, since even pure
liquids, according to a rule to be mentioned later (see p.
155), possess only a very small conductivity of their own.
1 The recent attempt of Roloff (Zeitschr. angew. Chem., 1902, Heft
22-24, also separately published by Springer, Berlin, 1902) to establish
a theoretical basis on the ground of the assumption of a variable disso-
ciation of the water itself stands in direct contradiction to the facts,
for the ionic product of water, even in concentrated solutions of electro-
lytes, has been found by the most "diverse methods (see p. 56) to be
entirely constant.
*3 2 the theory of electrolytic dissociation .
The held of these more concentrated solutions has
recently been the subject of interesting researches by
Wolf 1 and Rudorf, 2 whose results may best be dis-
cussed with the aid of one of the examples studied,
namely, that of acetic acid. It w ? as shown that the
addition of acetic acid to any electrolyte acts in such a
way as to reduce the mobility of the ions of the latter by
a definite amount, proportional to the concentration of the
acetic acid. This reduction of mobility is equal to about
9-3% P er normal strength of the acid, so that, for instance,
in a mixture of sodium chloride -hi -normal acetic acid
the conductivity of the sodium chloride, no matter in
what concentration it is present, is 9.3% less than in pure
water. Since this influence upon the mobility of ions has
shown itself to be entirely independent of their nature,
nothing is easier than to assume that the acetic acid also
affects the mobility of its own ions in the same measure,
so that in a 1 normal acetic acid, for example, the value
of the equivalent conductivity must again be less by
9.3% than if the same number of ions moved in pure
w'ater, as is the case at infinite dilution (A 0 ). In order,
therefore, to get at the real degree of dissociation, the
equivalent conductivity A for the high concentration is to
be increased by the correction due to the retarding in-
fluence which the presence of the undissociated acid
brings about. In fact, Abegg found that the constancy
of the expression
(Corr. J) 2 -c ^
A 0 -(A 0 ~Corr.A) = ConSt -
1 Zeitschr . physik . Chem ., 40 , 253 ( 1902 )..
2 Ibid ., 43 , 257 ( 1903 ).
EQUILIBRIA AMONG SEVERAL ELECTROLYTES . *33
is fulfilled up to considerably higher values for c than is
the case when the correction is not introduced. The
following values are taken from the investigation of
Rudorf, who took up the subject more exactly:
Acetic Acid (25 0 ). ^ 0 = 397 -
c
A
k (uncorr.)
Corr.-factor.
k (corr.)
0.019
12.3
1.88
1 . 002
i. 88
0.039
8-57
1.85
1.004
1.87
0.078
6.08
1 . 84
1. 007
1.87
°* I 57
4-23
1. 81
1.015
1.86
°- 3 T 3
2.97
1.76
1.C29
1.86
0.627
2.01
1 . 62
1.059
1.82
1-254
I.29
i -33 !
1. 11 8
r.67
The range of the reaction constants, or in other words
the field within which the affinity manifestations of the
ions possess the same intensity as in pure water or at
extreme dilution, extends in this case to about o. 6-normal
concentration. At higher concentrations where the con-
stant, even by introducing the corrected A value, assumes
other values than for dilute solutions, this deviation is
undoubtedly to be attributed to the changing of the
medium. And indeed I may draw the conclusion from
Rudorfis investigation just alluded to, that this constant,
variable with the medium, possesses the chemical signifi-
cance belonging to it according to its derivation; for the
same also regulates the ratios of the quantity of acetic
acid ions and the undissociated acid, when the acetate
ions are altered by the addition of strongly dissociated
acetates.
INFLUENCE OF PRESSURE AND TEMPERATURE
ON DISSOCIATION.
Now that we have considered in the preceding pages the
influence of concentration on the degree of dissociation of
electrolytes, the question arises, Upon what other addi-
tional influences is dissociation dependent? A general
answer is given by the so-called thermodynamic principle
of Le Chatelier, according to which, action on a system
in equilibrium by an agent from without brings about
a reaction that works against this external action. If,
then, we attempt to increase by compression the pressure
on such a system, that one of the two reactions in equi-
librium (decomposition into ions or combination of ions to
form undissociated molecules) will take place which gives
a diminution in volume, for thereby the condition of
stress in the system caused by the pressure is reduced. At
the suggestion of Arrhenius, a fine piece of research
pertaining to this influence was carried out by the Russian
Fanjung, 1 w T hom, we regret to say, death claimed all too
early. He worked with pressures as high as 260 atmos-
pheres. The observed increases in conductivity for the
highest pressures amount at most to about 9%, depending
upon how great is the volume-difference between the
1 Zeitschr. physik. Chem., 14 , 673 (1894).
INFLUENCE OF PRESSURE AND TEMPERATURE . i$5
undissociated and dissociated acids (mostly organic).
They are found to be in best agreement with the values
calculated from this volume-difference. It is plain to
see, however, that the pressure variations occurring in
every-day life have no effect in any way noteworthy on
the dissociation of electrolytes.
On the other hand, the influence that temperature
changes may have on dissociation is very marked. If we
wish to determine this from a study of the conductivities,
it is necessary, in the first place, to consider the super-
imposed influence of the changed ionic friction or ionic
mobility discussed on p. 35 and follow- ing pages. The
conductivity changes conditioned on mobility evidently
are not linked writh a temperature influence on the degree
of dissociation, for the variation in conductivity caused
by variation in temperature can be attributed, and in fact
in many cases is to be attributed, essentially to changed
ionic mobility, without the degree of dissociation of the
electrolyte having at the same time undergone any altera-
tion. To put it mathematically, in the expression
a=~* not only A but Aq as well is changed in the same
ratio by the temperature.
Again, the temperature influence on the dissociation is
given by applying the principle of Le Chatelier. The
addition of heat will alter the degree of dissociation in the
direction of that reaction which absorbs heat; that is, in
case the ionic dissociation is endothermic the dissociation
will increase upon heating; in case it is exothermic it will
decrease, A number of methods may be employed to
determine the heat effect of ionic decomposition or the
T 36 THE theory of electrolytic dissociation.
heat of dissociation (ionization), which are based on the
previously mentioned law of the thermo-neutrality of
strong electrolytes. According to this law, the mixing of
two electrolytes produces no heat effect when all of their
constituents continue in the ionic state after mixing.
Take, for example, the electrolytes KC2H3O2 and HC 1 ,
and let us assume, contrary to the facts, that upon mixing
they do not form imdissociated acetic acid, but that the
acetate' and H* ions continue to exist alongside of each
other; then in this case the mixing would not involve a
heat of reaction. However, the heat of reaction occurring
in reality is to be attributed directly to the circumstance
that H* and acetate' ions unite to produce undissociated
acetic acid, and so we have in this heat of reaction be-
tween potassium acetate and hydrochloric acid the imme-
diate heat effect of the formation of undissociated acetic
acid from its ions. The negative value would therefore
represent the heat of dissociation of acetic acid. This
method of determining the heat of dissociation may be
described as the mixing of two strongly dissociated com-
pounds, of which each contains one of the ionic com-
ponents of the weakly dissociated substance whose heat
of dissociation is sought, and which in the process of
mixing is formed in the undissociated state.
Another method, very similar in principle to the one
just mentioned, is based on the fact alluded to above
(see p. 59), that the neutralization of strong acids and
bases by one another always produces the same heat effect,
13700 cal. per gram-equivalent. Deviations from this
heat of neutralization, -which essentially represents the
heat effect of the formation of water from H* and OH 7
INFLUENCE OF PRESSURE AND TEMPERATURE . 137
ions, are to be found whenever weak acids or bases are
neutralized by one another, as the table below shoTvs.
The deviations explain themselves in that, in addition to
the formation of water, a further reaction takes place. Since
the neutral salt solution formed is strongly dissociated
according to the general rule, while before neutralization
one of its ionic components was appreciably undissociated,
being combined with one of the ions of water, it follows
that in such a neutralization a dissociation of the weak
electrolyte employed must result at the same time. The
equation of such a reaction will best elucidate the facts.
For that purpose let us consider, say, the neutralization of
NaOH by acetic acid, and assume as an approximation
that NaOH is completely dissociated, while only the
Heats of Neutralization.
(Thomsen.)
By NaOH.
Weak Acids.
Metaphosphoric acid . . 14300 cal.
Hypophosphorous acid. 15 100 “
Hydrofluoric acid 16300 tc
Acetic acid 13400 “
Chloracetic acid 1430° “
Dichloracetic acid 14800 11
Strong Acids .
HC 1 13700 cal.
HBr 13700 “
HCIO3 13800 “
HN 0 3 13700 “
By HC 1 .
Weak Bases .
Ammonia 12200 cal.
Methylamine 13100 tc
Dimethylamine 11800 <c
Trimethylamine. ..... 8700 * 4
Strong Bases .
LiOH 13800 cal.
NaOH 13700 “
Ba(OH) 2 13900 “
T etram ethy lammonium
hydroxide 13700 “
(small) fraction a per mole of the acetic acid is present
in the form of ions, and the larger portion (1 —a) is in
undissociated combination with the H* ions. If now we
13 s THE THEORY OF ELECTROLYTIC DISSOCIATION .
mix one mole of each of the two substances and write
the equation in such a way that we separate the ions and
undissociated portions from each other, then the neutrali-
zation equation will read:
i Na*-f i OH' -Fa H'4- a Acetate' 4 - (i — a)H acetate
= i Na* 4 -i Acetate' 4 - H 2 0 +a cal.
If we combine with it the further assumed equation
i N a* 4 - 1 OH' 4- 1 H‘ 4 -i Acetate'
= i Na* 4 -i Acetate' 4 - H2O 4 - 1 3 700 cal.,
which would apply if acetic acid were a strong, almost
completely dissociated acid, we get, by subtracting the
first equation from the second, the following simple
expression :
(1 — a) H ' 4- (1 — a) Acetate'
= (1 —a) H acetate 4- (13700 — a) cal.
or
H acetate =H* 4 - Acetate ' 4 — cal.
1 —a
That is, the observed heat of reaction a diminished by
13700 cal. represents the heat of dissociation for i—a
moles of the weak acid or base when we neutralize the
same by a strong base or acid and divide the heat effect,
diminished by 13700 cal., by i—a . With a weak acid
1 — a=i , very nearly, a being very small.
Experimentally this way of obtaining the heat of dis-
sociation is not very advantageous, because it generally
gives the sought magnitude as a small difference of two
INFLUENCE OF PRESSURE AND TEMPERATURE . 139
large heat effects, so that the experimental errors play
a very important part in this difference. It is unlike the
previous method in that we start with the weakly dis-
sociated compound and end with the strongly dissociated
salt of the same; that is, to a certain extent it is the
reverse of the first, in which we prepare the undissociated
substance from the strongly dissociated salt by means of
a strongly dissociated acid or base. The heats of disso-
ciation obtained by either of these two methods may
serve to calculate the influence of temperature change on
the degree of dissociation by employing the thermodynamic
equation derived by Arrhenius, 1
dink W
dT ~~ RT 2 9
in which k signifies the dissociation constant, W the heat
of dissociation, T the absolute temperature, and R the
gas constant in calorimetric units (1.99).
It is true Arrhenius followed the reverse course, in that
he calculated the heat of dissociation W from the vari-
ability with the temperature of the conductivity or of the
dissociation constant k, and compared it with the results
obtained by the methods indicated above. From these
conceptions of Arrhenius it was possible to predict an
interesting case of conductivity: that with electrolytes
whose heat of dissociation is strongly positive,- rise in
temperature is followed by such marked reduction in the
degree of dissociation that the increase in conductivity
resulting from the enhanced ionic mobility is covered up.
In fact, in this way it has been possible, in cases like
1 Zeitschr. phy$ik, Cbem., 9 , 339 (1892).
140 THE THEORY OF ELECTROLYTIC DISSOCIATION.
phosphoric and hypophosphorous acids, to establish
experimentally such reductions in conductivity. This
was the more striking since it was generally thought that
the characteristic difference between electrolytic and
metallic conductivity was the negative temperature
coefficient of the latter, i.e., reduction in conductivity
with rise in temperature.
In the following table a series of heats of dissociation is
given, from a consideration of which, however, nothing
in the way of a relationship between these values and the
chemical nature of the substances has resulted. It is
worthy of note nevertheless that they are all markedly
variable with the temperature.
Heats of Dissociation.
(Arrhenius, 1SS9, 1S92; Thomsen, 1SS2; Baur, 1897.)
(Exothermic dissociation taken negative, as is customary in
thermodynamics.)
35 ° 21.5 0
Acetic acid — 386 cal. +28 cal
Propionic acid — 557 “ — 183 44
Butyric acid — 935 44 — 427 44
Succinic acid 4- 445 “ +1115“
Dichloracetic acid — 2893 4 ‘ — 2924 4 *
Phosphoric acid — 2458 44 — 2103 44
Hypophosphorous acid — 4301 * * — 3745 * 4
Hydrofluoric acid — 3549 * * . —
Water (xo. 14 0 ) 4- 14247 44 ■ (24.6°) + 13627 44
Interpolation-formula: - °° after Kohlrausch and Hevdweiller.*
(273+/)
i
1 5°
r 5°
25°
35°
Nitrourea
•••i +5477
4-3812
+3640
Nitrourethane
+3665
+ 3724
+ 2943
4-2260
Amidotetrazole ....
-•* T-J724
+5 2 5 s
-1-4593
+3865
INFLUENCE OF PRESSURE AND TEMPERATURE . I 4 1
The heat effects are in part positive, in part negative, and
in many instances quite small, which is in keeping with
the fact that frequently the dissociation into ions takes
place without very great energy changes. The heats of
dissociation of salts as calculated by Arrhenius are to be
looked upon as uncertain, for the reason that (see p. 121)
we are still in doubt on the dissociation of the same as
calculated from the conductivities. The substances of
special interest are those with very great heat of dissocia-
tion, because this corresponds to a great variation of the
degree of dissociation with the temperature, as we saw
above from the conductivities of the two acids of phos-
phorus. The most interesting substance in this regard,
because the most extreme, is water, whose decomposition
into ions absorbs the enormous quantity of 13700 cal. of
heat. From this, according to the equation of Arrhenius,
we can predict that the usually small temperature in-
fluence on the dissociation, and therewith on the con-
ductivity, must be abnormally great in the case of water.
Kohlrausch and Heydweiller, in their previously men-
tioned investigation, had occasion to test this conclusion
of the dissociation theory. They calculated the tem-
perature coefficient of the conductivity of pure water by
the equation of Arrhenius and found it to be 5.8% per
1 0 , 1 while the otherwise largest known temperature co-
efficients are those of the salts, which at most scarcely
amount to one hah as much. The investigators named
found the highest value for the temperature influence on
the conductivity of water, that is, the influence peculiar to
1 Wied. Ana., 53 ,. 231 (1894).
142 THE THEORY OF ELECTROLYTIC DISSOCIATION .
water least contaminated, to be 5.3%. and they were able
to calculate, by means of the deviation of this value from
that theoretically found, that the purest water obtained
by them still contained impurities to the extent of several
thousandths of a milligram per liter. For the pure water
the observations gave conductivities at the different tem-
peratures which led to the degrees of dissociation con-
tained in the following table:
Dissociation of Water at Different Temperatures.
(Kohlrausch and Heydweiller, 1S94.)
O)
0
I O 0 j lS° ; 20° j
34 °
42 0
50 °
roo°
Ionic concentra-
tion/Liter. . .
k w !
I 1
i c * 35°*39
O. 120. 15
i i |
A 0 i i
0.56:0.80 1.09:
O.3TI0.64 1.2
! .■ j
1 - 47
2- 15
i -93
3-7
2.48
6.15
8.5
72.O
xio-’
Xio- u
i
We see how rapidly the dissociation of the water rises
with the temperature, and that, for example, at 50° it is
already more than three times greater than at the ordinary
temperature. For the phenomenon of hydrolysis this
fact is of very great importance, since, as we saw (p. 76),
the degree of hydrolysis is determined by the ionic con-
centration raised to the second power, which is the water
constant k w . Correspondingly, hydrolysis greatly increases
at higher temperatures. A whole series of chemical
experiences . may be explained on this basis. If, for
example, we color a neutral ammonium salt solution with
litmus and heat it, w r e observe that at higher temperatures
a distinct red color sets in, indicative of the fact that an
‘appreciable quantity of free hydrochloric acid has been
INFLUENCE OF PRESSURE AND TEMPERATURE 143
separated, or, in the language of the dissociation theory,
undissociated ammonium hydroxide has been formed
from the ammonium ions and the hydroxyl ions of the
water. A further phenomenon belonging here and
made use of in analysis is the precipitation of difficultly
soluble hydroxides by inducing the hydrolysis of their
weak salts. This happens, for instance, in the precipitation
of basic ferric acetate from a solution of ferric chloride by
an alkali-acetate, and it may be of interest to consider this
action somewhat more in detail. These last two salts
we may look upon as markedly dissociated, notwithstand-
ing the fact that the ferric chloride is considerably hydro-
lyzed on account of the weakness of its base, and so mixing
them gives the ferric ions an opportunity to combine with
the acetate ions. We have before us, then, such an
electrolytic combination of two w r eak ions as was described
on p. 89. The H‘ ions, that in the. case of the chloride
bring the hydrolysis to a standstill, are checked in their
formation by the acetate ions present, and in consequence
hydrolysis sets in to a considerably greater extent and
leads to the formation of a much larger amount of basic
ferric acetate along 'with undissociated acetic acid. The
raising of the temperature favors still further this hydrol-
ysis, so that w r e are in position to increase the concen-
tration of the undissociated ferric hydroxide to such a
point that the solvent capacity of the wrater for this
substance is passed, the solution becomes saturated, and
all further formed hydroxide must precipitate. Chromic
hydroxide and aluminium hydroxide, as is well known, are
also precipitated by the hydrolysis of their solutions
containing acetate.
144 THE THEORY OF ELECTROLYTIC DISSOCIATION.
To return once more briefly to heats of dissociation, the
following deserves mention. In a number of cases it has
been found that organic substances which are capable of
acting either as an acid or a base must, before splitting up
into ions, undergo a molecular rearrangement, that is,
change into an isomeric form. We are indebted to the
interesting investigations of Hantzsch for an entire series
of examples of such so-called pseudo acids and bases,
which in dissociating suffer this sort of rearrangement, and
it seems as though in all of these electrolytic substances
the heats of dissociation are especially large. These
heats of dissociation manifest themselves either in the
great variation of the degree of dissociation and the
conductivity with the temperature, or in the heats of
neutralization of these substances deviating considerably
from the value 13700 cal. While there seem to be as
yet no investigations pertaining to the latter fact, violuric
acid and oximido-oxazolon offer two cases of the first kind,
for which Guinchard 1 determined the variation of the
dissociation constants with the temperature, and by
means of this the heat of dissociation of violuric acid is
calculated to be 3700 cal. 2
The reaction of the intermolecular rearrangement
preceding the dissociation must of course produce a
certain heat effect, which appears as a part of the heat of
dissociation. It is likely, therefore, that we are permitted
to generalize to the extent of saying that intermolecular
reaction and high heat of dissociation are bound together
1 Ber. d. deutsch. chein. Ges., 32 , 1723 (1899).
? Ibid., 33 , 393 (1900}.
INFLUENCE OF PRESSURE AND TEMPERATURE. 145
by a common cause. This holds without doubt not only
for the two cases mentioned above, but in all probability
for two other cases of high heat of dissociation given in the
table (p. 140}, namely, hydrofluoric acid and water, since
hydrofluoric acid is essentially present in the form of the
molecules H 2 F 2 , not only in the gaseous state but also in
solution, 1 and must pass through the intermolecular
reaction
H2F0-2HF
in order to dissociate into the ions H' and F'. Also
in the case of water a similar intermolecular reaction is
more than probable, for the most varied facts have led
to the conclusion that the water molecules in the liquid
state are exceedingly strongly polymerized, so that they
must likewise first break up into simple molecules of the
formula H 2 0 in order to form H* and OH' ions. We can-
not, however, consider this relation between high heat of
dissociation and inner reaction as altogether general,
because the phenols and a number of other substances
likewise show r high heats of dissociation 2 without indi-
cations of the probability of intermolecular reactions. It
seems of importance, nevertheless, that the fact of the
presence of great heat of dissociation has recently led
Hantzsch 3 to make the interesting discovery that the salts
of phosphorous acid are capable of existing in the form
1 See Jaeger, Zeitschr. anorg. Chem., 27 , 28 (1901); Abeggand Herz,
ibid.. 35 , 129 (1903).
2 See Hantzsch, Ber. d. deutsch. chem. Ges., 32 , 3073 (1899;.
s Zeitschr. f. Elektrochem., $, 4S4 (1902).
146 THE THEORY OF ELECTROLYTIC DISSOCIATION..
of two structural isomers. That is, phosphorous acid
also exists in two isomers of tautomeric form, and so for
this acid it likewise appears that high heat of dissociation
(great temperature coefficient of the conductivity, Arrhe-
nius) is bound up with the possibility of intermolecular
reaction.
NON-AQUEOUS SOLUTIONS.
All our previous discussions concerning dissociation
have been confined to solutions in which -water was the
solvent. This was done not alone for the reason that the
investigation of dissociation and conductivity was first
carried through on aqueous solutions, but because here
we have arrived at comparatively simple results, and
because the property of behaving as an electrolyte is an
especially conspicuous peculiarity of the particular
compounds when dissolved in water. The capacity for
ionic decomposition of those substances which have been
recognized as electrolytes in water also makes its ap-
pearance more or less distinctly in other solvents. In
fact, the nature of the solvent plays an exceedingly
important role, so that it has been possible to arrange the
various media in a series according to their “ dissociat-
ing ” power, which series agrees for most solutes.
One important advance in the question as to what other
physical or chemical properties of substances the dis-
sociating power of solvents is associated with was made
by Nemst 1 and Thomson, and is based on a consideration
of the dielectric constant. This constant of a medium is
characteristic of the force with w T hich two electrically
charged bodies within this medium attract or repel each
other; the greater the constant is the smaller becomes the
1 Zeitschr. physik. Chem., 13 , 531 (1894).
*47
14& THE THEORY OF ELECTROLYTIC DISSOCIATION,
mutual force manifest between the electrically charged
particles, the distance between the same remaining equal.
Now the ions are also to be considered as such electrically
charged parts, and accordingly the forces of attraction
between the ions must become smaller, and their separa-
tion from one another easier, the higher the dielectric
constant of the medium is. It follows that the dissociation
of substances should be especially great in that medium
with the highest dielectric constant. In the table are
given the dielectric constants of a number of substances
at ordinary temperature.
Dielectric Constants . 1
Hydrocyanic acid, HCN 95 .0
Hydrogen peroxide, H 2 0 2 92.8
Water, BUO 81.0
Formic acid, HCOOH 57.0
Acetonitrile, CH 3 CN 36.4
Nitrobenzene, C 6 H 5 N0 2 34 .0
Methyl alcohol, CH3OH 32.5
Propionitrile, C 2 H 5 CN .....* 26.5
Benzonitrile, C 6 H 5 CN 26.0
Ethyl alcohol, C 2 H 5 OH 22.0
Liquefied ammonia, NHg 22.0 (—34°)
Acetone, (CH 3 ) 2 CO 20.7
Glycerine, C 3 H 5 (OH) 3 16.5
Liquefied sulphur dioxide, S0 2 14.8
Pyridine, C 5 H 5 N 12.4
Aniline, C 6 H 5 NH2 7.2
Acetic acid, CH 3 COOH 6.5
Chloroform, CHC1 3 5.0
Ether, (CoH 5 ) 2 0 4.4
Benzene, C fi H 6 . . 2.3
1 Schlundt, Journ. Physic. Chem., o, 165 (1901). — Drude, Zeitschr.
physik. Chem., 23, 308 (1897). — Linde, Wied. Ann., 56, 563c 1895). — -
Goodwin and de Kay Thompson, Phys. Review, 8, 38 (1899). — Calvert,
Drud. Ann., 1, 483 (1900). — Coolidge, Wied. Ann., 69, 125 (1899). —
Mathews, Bibliography of Dielect. Consts., Joum. Physic. Chem., 9 ,
667 (1905).
NON-AOUEOUS SOLUTIONS. 149
We see hereby that water must possess an abnormally
high power of dissociation, since of all common solvents it
has by far the greatest dielectric constant, and in general
it seems that the order given in the table agrees approx-
imately with that found in studying the ionic dissociation
of electrolytes in various solvents by means of the con-
ductivities. Of especial interest in this connection is an
investigation of Centnerszwer, 1 who found the equivalent
conductivities of potassium iodide and trimethyl sulphine
iodide in HCN at o° to be about four times as great as
the corresponding figures for aqueous solutions. This is
about as great as the equivalent conductivities of the
best-conducting electrolytes, the acids in water solutions
at 25 0 , and even if it does not necessarily follow (see later
on) that the dissociation is greater than in w T ater, never-
theless this is at least possible. If such were the case,
it would be in best agreement with what one must expect
according to the high dielectric constant of HCN.
On the other hand, however, these investigations have
evidently shown that the dielectric constant cannot alone
be the determining factor for the dissociation; moreover,
purely chemical questions seem to be very vitally con-
cerned. For example, according to the table of dielectric
constants, it was to be expected that the solutions in
benzonitrile and propionitrile would be equally dissociated
and consequently also would show about the same
conductivity. A comparison by Schlundt 2 of the con-
ductivities of silver nitrate in these two dielectrically
1 Zeitschr. physik. Chem., 39 , 217 (1902).
2 Joum. Physic. Chem., 5 , 168 (1901).
*50 THE THEORY OF ELECTROLYTIC DISSOCIATION.
equal solvents, as measured by Lincoln, and Dutoit, gave
large differences in the sense that the conductivity in
propionitrile corresponds to a markedly greater ionic
concentration. This fact and others are strikingly in
accord with another assumption as to the reason for the
difference in dissociating power, brought forward by
Dutoit , 1 namely, the ability of the solvent to associate,
forming polymerized molecules. Bruhl , 2 for his part,
finds a connection with the question whether or not the
solutions contain atoms whose valences in the compound
are not as yet completely saturated. These two views
seem to me to mean practically the same thing, for the
reason that evidently the ability to associate is conditioned
upon the presence of unsaturated valences. For the two
nitriles mentioned, the view that polymerization plays a
part agrees excellently with the facts, in so far as the
researches of Ramsay and Shields 3 have shown that
propionitrile is considerably polymerized, while benzoni-
trile does not associate. The conclusions pertaining to
ionic dissociation, derived from the conductivities in these
non-aqueous solvents, are subject to considerable un-
certainty, because in only a few' cases and for only a few
electrolytes have wre been able to determine the values for
Ao, the limit value of the equivalent conductivity for great
dilution. Therefore the absolute values of the equivalent
conductivity give only a very uncertain approximation for
the degree of dissociation, and, strictly speaking, express
1 Compt. rend., 125 , 240; Bull. soc. chim. (3), 19 , 321 (1898).
2 Ber. d. deutsch. chem. Ges., 28 , 2866 (1S95); Zeitschr. physlk.
Chem., 27 , 319 (1898); 30 , 1 (1899).
3 Zeitschr. physik. Chem., 12 , 433 (1893).
N6N-AQUE0US SOLUTIONS.
151
nothing more than that there are ions present in a solution,
and in what way the number of ions varies in the same
solvent with varying concentration, A comparison of dif-
ferent solvents with one another is altogether impossible
under these conditions, since the conductivities (see p. 29)
are dependent not only on the degree of dissociation but also
very much upon the mobility of the ions, and this mobility
stands in an entirely unknown relation to the nature of the
solvent. For that reason the attempt has been made to
employ the other method which in the case of aqueous
solutions has been found to be serviceable, namely, to
measure the degree of dissociation in these solvents by
means of the osmotic pressures (from freezing-point,
boiling-point, or vapor-pressure determinations). And
indeed in many cases, for example solutions in the various
alcohols, it has been demonstrated that electrolytes, or
substances which possess conductivity in these solvents,
also show an increased molar number (an abnormality
factor i> 1), as, is to be expected from the expression
previously derived (see p. 9),
i=i + (n— i)*a.
However, not only have i values been found (by osmotic
methods) which appear much too small to be made to
harmonize with the uncertain degrees of dissociation
derived from the a values (electrically determined), but
in a number of cases i values have been obtained that are
even smaller than 1, in spite of the fact that the presence
of conductivity proves the presence of an appreciable
degree of dissociation. These facts, which have unneces-
sarily aw T akened doubt as to the foundations of the
* 5 * THE THEORY OF ELECTROLYTIC DISSOCIATION.
dissociation theory , 1 give us a clue to wherein consists the
explanation of the anomalous behavior of the non-aqueous
solutions. We may, for instance, maintain the relation
between i and a if we admit the possibility that the
undissociated molecules of the electrolyte associate to
form polymerized molecules. Measurements have shown
polymerization to be true of many other substances, and,
for example, with organic acids this phenomenon has been
repeatedly verified by the extensive investigations of
Beckmann and others. With such association it is of
course very* possible that the reduction in the number of
molecules caused thereby is greater than the increase
which has its origin in the ionic decomposition. In this
way for the present we can give an entirely satisfactory
qualitative explanation for the seemingly very complicated
relations of non-aqueous solutions. Likewise in keeping
with this, as Nemst has already stated, is the fact that the
serial order of the dissociating powers of solvents is the
same, whether we base it on the electrolytic dissociation
of simple molecules into ions or the non-electrolytic
1 See, for example, Joum. Physic. Chem., 5 , 339 (1901). The author
Kahlenberg is an enthusiastic opponent of the ionic theory, collecting
facts with energy and great experimental skill which appear unexplain-
able by the theory. The possibility of suitably expanding the theory
he unfortunately does not consider. It seems without purpose, however*
to discard a theory so broadly established without putting a better one
in its place. We are not accustomed to tearing down a habitable house
because a few rooms are illy lighted, and putting ourselves out on the
street, unless it be we can move into a better one. Any theory which
desires to depose the one of Arrhenius has at the very outset the dif-
ficult task of bringing into a common field of view all the manifold facts
which Arrhenius has taught us to summarize.
NON-AQUEOUS SOLUTIONS . 153
dissociation of polymerized molecules into simple ones.
Accordingly, with decreasing power of dissociation, we
must have, in non-aqueous solvents, as compared with
water, not only a decrease of the dissociation into ions but
also a decrease of the dissociation of polymerized molecules
into simple ones, or, conversely expressed, the association
into polymerized molecules must be favored. Whether
the in part unsatisfactory agreement between the degrees
of dissociation of aqueous solutions, as determined by
osmotic and electric methods, can find an analogous
explanation is still an open question. At any rate, it is
worthy of note, as the approximate agreement proves,
that in water association evidently seems to play quite a
secondary role.
It is well to add that the probability of a participation
of the solvent in the process of ionic dissociation, such as
the formation of an addition product of solvent and ions,
is variously supported by the experience with non-aqueous
solutions. The assumption that the presence of free
valences assists in determining the dissociation led Briihl to
the conclusion that the ions are hydrated; and the results
of Walden, that iodides and sulphocyanates have especially
high solubilities in SO2, with peculiar colorations of their
SO2 solutions, indicating the formation of new com-
pounds , 1 point to the same conclusion. That this agrees
with the facts is shown in a research by Fox , 2 who also
proved the existence in aqueous solutions of such complex
ions of the halogens and other anions with S 0 2 . The
1 Zeitschr. physik. Chem., 42 , 432 (1903).
1 Dissert., Breslau, 1902 ; Zeitschr. physik. Chem., 41 , 458 (1902).
154 THE THEORY OF ELECTROLYTIC DISSOCIATION.
general result of the knowledge gathered thus far with
non-aqueous solutions may for the present be summed up
to the effect that the simplicity of conditions prevalent in
aqueous solutions is here very much complicated by the
phenomenon of the association of the non-ionized portion
of the electrolyte. Hence the problems to be solved in
this connection are, first, the determination of the amount
of association of the electrolytes and, next, the Kohlrausch
law for the additive nature of Jo- According to the
equilibrium laws, it is no doubt permissible to assume
that in non-aqueous solutions the ionic splitting-up,
though in any case probably very slight, is caused by the
great reduction, due to association, of the active masses
of the simple molecules that alone are capable of ionizing.
No doubt we might assert with equal right that in water
the active mass of the undissociated molecules becomes too
small, on account of the great ionization, to allow an
appreciable association, since this latter is again pro-
portional to the active mass of the simple molecules.
But in many instances, for example with the organic
carboxylic acids, the electrolytic dissociation is so slight
even in water that the active mass of the undissociated
molecules is not appreciably affected by it; that is, even
if ionization is wanting, association would not increase in
a sensible degree. ' So that in such cases we also find the
association in water exceedingly small as compared with
the other solvents, for which, according to the researches of
Beckmann, the organic acids and alcohols already alluded
to give the best evidence. This leads one to the assump-
tion that the phenomenon of association is the chief
phenomenon, and that ionization in non-aqueous solu-
NON-AQUEOUS SOLUTIONS. 155
tions is so small, as a rule, essentially because of the great
amount of association.
Finally, we may consider that case which deals with the
amount of dissociation in pure substances as one of non-
aqueous solvents, or, as we may term it, one of self -disso-
ciation. Here it is a general rule that the electrolytic
conductivity of pure substances is without exception
exceedingly small, though, according to Walden, 1 it seems
to increase with the polar difference of the atomic com-
ponents. The amount of self-dissociation of water and
the conductivity resulting therefrom have already been
discussed (see p. 56). Conductivities of about the same
order of magnitude have been observed for a whole series
of other liquids of greatest possible purity, such as methyl
and ethyl alcohol, sulphur dioxide, liquid ammonia, etc.
But judging by the experiences of Kohlrausch and
Heydweiller with water, it is difficult to say in how far
the conductivities thus obtained are those of the absolutely
pure substances, or to what extent possibly they are
conditioned upon electrolytic impurities. It is worth
mentioning in this connection that such substances as
sulphuric acid, hydrochloric acid, etc., which in aqueous
solutions belong to the best electrolytes, in the pure liquid
form, on the contrary, possess an exceedingly small con-
ductivity. The only known exceptions to this are the
salts which in the melted state, that is as liquids, are very
good electric conductors. It may be that this behavior
is connected with a large dielectric constant of the salts in
1 Zeitschr. anorg. Chem., 25 , 225 (1S90); see also Abegg, Christiania
Vidensk. Selsk. Skrifter, 1902, No. 12, p. 8.
I5 6 the theory of electrolytic dissociation .
the molten state, although it has not been possible thus far
to determine the same. In the solid state they show
dielectric constants between 6 and 7, while all other solid
substances, even water in the form of ice, 1 show only
1 to 3; and since liquids and melts always have higher
dielectric constants, it does not seem improbable that
the salt melts are exceedingly strong dielectrics. From
this follows the probably very great self-dissociation which
lies at the basis of the good conductivity of the salts, and
according to the Thomson-Nemst rule is determined by
their high dielectric constant. It is true at the high
temperatures of the melted salts the ionic mobilities may
be so great that it may not be necessary to consider the
good conductivity as due to a marked dissociation.
Especially in the case of water, where, as a result of the
high dielectric constant, one might expect a greater self-
dissociation, the very great association is in all likelihood
essentially to blame, which takes away the simple mole-
cules, the real material for the ionization.
The determination of electrolytic dissociation based
solely on conductivities, however, without knowledge of
the specific resistances which the medium opposes to the
transport of ions, must always be looked upon as extremely
uncertain. So, for instance, the view has been frequently
expressed or entertained that the salts in the solid form are
not electrolytes, or at most possess only a very slight
electrolytic dissociation. This is probably based on the
observation that the solid salts have an exceedingly slight,
1 See Abegg, Wied. Ann., 65 , 229 (189S), and Zeitschr. f, Elektro-
chem., 5 , 353 (1899).
NON-AOUEOUS SOLUTIONS .
I 57
but nevertheless perfectly definite, conductivity, as
determined by Warburg. The color of many solid salts,
especially when they crystallize as hydrates, is very often
identical with the specific ionic color of the chromophore
constituent, and thus makes the presence of ions probable.
The small conductivity in spite of the ions may easily be
explained by the enormous frictional resistance to which
the moving particles in their solids are subjected. The
greatest promise of success in penetrating into the quanti-
tative dissociation relations of non- aqueous solutions
seems to be offered by studies in gradually varying
solvents, as an example of which the research of Wolf,
mentioned above (p. 132), may be cited. The first in-
vestigation with this object in view comes from Arrhe-
nius, 1 who studied the influence of small amounts of
non-conductors, such as alcohol, sugar, etc., on the
conductivity and dissociation of various electrolytes.
The chief result of this investigation is the establishing of
the fact that the changing of the solvent also produces
changes in the degree of dissociation, but of very different
amounts, according to the nature of the electrolyte. The
strongest dissociated electrolytes are affected very little
in their degree of dissociation by slight changes of the
medium, while the weak electrolytes are extremely
sensitive to such changes, their degree of dissociation
being reduced. Cohen 2 has confirmed the results of
Arrhenius for strong electrolytes in the entire interval of
solvent produced by mixing alcohol and water in various
1 Zeitschr. physik. Chem., 9 , 487 (1892).
2 Ibid., 25 , 1 (1S99).
I 5 8 THE theory of electrolytic dissociation.
proportions. He found that the degrees of dissociation
in these cases do not seem to be influenced by the medium,
at least in so far as the conductivity represents a correct
measure of dissociation. We see, therefore, that it is less
the nature of the solvent than that of the dissolved sub-
stance which is of influence here, and this leads us to a
final consideration, whose subject is the important
question, What sort of regularities exist between the
endeavor of the electrolytes to dissociate and the nature
of their components ?
CHEMICAL NATURE AND IONIZATION
TENDENCY OF THE ELEMENTS.
It has become apparent that of the elementary substances
an entire series appears altogether, or at least by evident
preference, in the form of ions. Thus, for example, there
is not a single compound of the alkali and alkaline-earth
metals which does not contain these metals for the greater
part as independent ions, while others, again, such as most
of the elements belonging to the carbon and nitrogen groups
of the periodic system, are as good as unknown in the
form of elementary ions. Furthermore, the difference in
capacity for forming positive and negative ions is very
striking: elements such as fluorine and chlorine never
appear as positive ions, while the elements of the first two
groups of the periodic system act exclusively as positive
ions In the middle groups the tendency to form ions
disappears more and more, in place of which these
elements assume an amphoteric character in that they
give evidence of a participation in the ion formation of
others combined with them, even though it has not been
possible thus far to confirm an independent formation of
ions.
A good illustration of the preceding statement is offered
by nitrogen, which combined with four H atoms furnishes
159
i6o the theory of electrolytic dissociation .
the cathion NH 4 ‘ (ammonium), while in the form of HN 3
orHN0 3 it produces the anions N 3 ' andN0 3 ' respectively.
Likewise phosphorus forms cathions in the phosphonium
compounds as well as anions in the acids of phosphorus
and the phosphides, 1 and again, sulphur shows a varying
polar behavior in the sulphine bases and in sulphides or
sulphuric acids. Furthermore, we are familiar with iodine
independent, and also as an anion-former in many com-
plex combinations, but nevertheless in addition it is' capa-
ble, as taught by the existence of iodonium bases, of enter-
ing into the garb of a cathion. 2 It is possible in general to
1 Schenck, Ber. d. deutsch. chem. Ges., 36 , 979 (1903).
2 Of such amphoteric electrolytes there are quite a number; thus,
almost all hydroxides of the weak positive elements along with oxygen
can form anions, so that their hydroxides are capable of producing
simultaneously cathions of the element and anions of its oxygen complex.
Among others, this is known to be the case with Pb(OH) 2 , Al(OH) 3 ,
Cr(OH) 3 , As(OH) 3 , As(OH) 5 , Be(OH) 2 , Sn(OH) 2 , Ge(OH) 2 (cf.
Hantzsch, Zeitschr. anorg. Chem., 30 , 289 [1902]; McCay, Journ. Amer.
Chem. Soc., 24 , 667 [1902]), and is deserving of interest because upon
dissociation OH' ions are formed on the one hand and H* ions on the
other, whose mutual concentrations in the presence of water are limited
by the water constant k w (see p. 55). In the coupled equilibrium,
such as, for instance,
Pb** + 2OH' ^ Pb(OH) 2 H* -f Pb 0 2 H',
an addition of strong bases (OH' ions) retards the production of Pb** on
account of the common OH' ions, that is, forces back the basic function
of the hydroxide, while the consumption of H* ions (as a result of the
formation of water) increases the concentration of Pb 0 2 ". In short,
the add nature (anion formation) is enticed forth, so to speak, which
agrees with the experience on other amphoteric substances. It is also
worth while to call spedal attention to the reaction, mentioned above
(see p. 1 17), of boric acid with fluorides, in which the OH' concentration
for the complex fluorides is brought forth by the consumption of the
CHEMICAL NATURE OF THE ELEMENTS . 161
confirm, by reference to the periodic system, the fact that
the tendency in each principal group to form cathions
increases with increase in the atomic weight, or, what is
the same thing, the tendency to form anions increases
with diminishing atomic weight. In the horizontal rows,
however, the tendency toward the formation of cathions
diminishes with increasing atomic weight. Quantitative
knowledge, at least of an approximate nature, is given
by the study of the electromotive activity of the elements
and of the decomposition voltages, or the amount of
electrical energy necessary to deprive an ion of its charge.
Not wishing to go farther here into these interesting
questions, suffice it to refer again to the previously men-
tioned articles of Abegg and Bodlander on Electro-
affinity, and Abegg on Valence. 1 Be it only noted that
the tendency to form ions, or the electro-affinity, manifests
itself also in the solubility relations 2 of the electrolytes
and their capacity for forming complexes; that is, the
disinclination to form ions is often associated with slight
aqueous solubility or with great tendency to enter into
complex ions, whereby the compound avoids the necessity
of being subjected to the dissociating force of the water.
The observation that all reactions in which ions
participate in measurable amounts — even the hydrolytic
borate ions. This indicates the presence of a weak basic nature in
boric acid. A number of organic amphoteric electrolytes have been
more carefully studied by Winkelblech (see p. 55, alanine, amido.
benzoic acid).
1 Zeitschr anorg Chem., 20 , 453 (1899); Christiania Vidensk. Selsk.
Skrifter, 1902, No. 12, p 8.
* Cl. Imnjerwahr, Zeitschr. f. EJektrochem,, 7 477 (1901),
162 THE THEORY OF ELECTROLYTIC DISSOCIATION.
actions of the exceedingly weakly dissociated water —
proceed to their equilibrium with an immeasurably
great velocity has induced the assumption that indeed
every capacity to react is to be attributed to the presence
of ions. A basis for this assumption has been thought to
exist in the fact that reactions between non-electrolytes
usually proceed with extreme slowness, corresponding to an
immeasurably small, but not altogether lacking, dissocia-
tion. We may, by way of illustration, consider the hydrol-
ysis of stannous chloride and stannic chloride. Both are
dependent upon the action of the OH' ions of the water
on the tin of the compound. The SnCl 2 , which shows
the presence of appreciable quantities of tin ions by the
fact that during electrolysis metal separates as a result of
the discharge of these ions, attains its state of hydrolytic
equilibrium momentarily; while, on the other hand, the
SnCU contains no demonstrable — or rather extremely
small — amounts of tin ions, and accordingly its hydrolysis
goes on very slowly, as traced by Kowalevsky . 1 Analogous
facts hold for the hydrolysis of PtCU and AUCI 3 , also for
the hydrolytic splitting-up of the esters , 2 as observed by"
Kohlrausch . 3 The exceedingly interesting investigations
of Brereton Baker 4 on the failure of gases to react when
absolutely dry, as well as the non-dissociation of NH 4 C1
and of Hg 2 Cl 2 , the failure of NH 3 and HC1, H 2 and Cl 2 ,
1 Zeitschr. anorg. Chem., 23 , i (1900).
2 Zeitschr. physik, Chem., 36 , 641 (1901).
3 Ibid., 33 , 1257 (1900).
4 Joum. Chem. Soc., 73 , 422; 77 , 646; 81 , 400 (1899-1902). See %lso
Noyes, Zeitschr. physik. Chem., 41 , n (1902).
CHEMICAL NATURE OF THE ELEMENTS . 163
and H 2 and 0 2 to react, and lastly the lack of electric
conductivity, which we attribute to ionization— all this
speaks likewise in favor of the assumption that capacity
for reaction is due to ions.
A more recent investigation of Kahlenberg, 1 which offers
as evidence against the above the instantaneous pre-
cipitations in non-aqueous solutions possessing no demon-
strable conductivity, should be completed in the direction
of striving to attain by all known means the absolute
dryness so difficult to accomplish, as the experience of
Baker shows. Until that has been done, we may only
conclude that very great reaction velocities can be reached
even with quantities of ions so small as to be beyond
detection, and it would depend upon penetrating into the
region of these small ionic concentrations, thus far in-
accessible, in such a manner as to measure their small
concentrations.
The dissociation theory has taught us to consider from
a common point of view and to understand in their mutual
relations an immense number of facts coming from the
apparently most diverse regions of chemistry. Doubtless
an equally great number of problems this theory has
presented to science and has helped or helps in their
solution. Its successes in the field of chemistry are no
greater than in the field of physics, where the brilliant
researches of Nemst have solved with its assistance the
theory of diffusion and the hundred-year-old problem
of the voltaic chain. Yes, one cannot resist the impres-
sion that the future of the theory will lead us directly to
1 Joum. PKysic. Chem., 6, 1 (1902).
164 THE THEORY OF ELECTROLYTIC DISSOCIATION.
the ultimate questions of chemistry, the essence of
valence and the affinity forces; and so one can maintain
that this conception of Arrhenius is one of the most
significant and fruitful with which theoretical chemistry
has ever been favored.
INDEX.
PAGE
Abegg. 123
degrees of dissociation from freezing-points and equivalent con-
ductivities 45
dilution equation, concentrated solutions \ 132
see Bersch - 116
valence 161
and Boildnder 127
electroaffinity 161
Absorption spectra of ions, Ostwald 12
Acid reaction on mixing neutral and alkaline compounds 117
Acids, and bases, neutralization of 58
avidity of, Ostwald , Arrhenius , Wolf 99
catalysis of cane-sugar in the presence of neutral salts 72
conductivity temperature coefficients 36
definition of 5
dibasic dissociation 51, 53
influence of substitution on strength of 47
liberation from salts 75
pseudo, Hantzsch 144
Additive properties of solutions 12
Alkaline reaction of difficultly soluble oxides and neutral salts, Bersch ,
Ahegg, 1 16
Ammonia, solvent action of 115
Amphoteric electrolytes 160
Anion, slowest 35
Anions, mobilities of organic 34
Anomaly of strong electrolytes 121
*65
INDEX.
1 66
PAGE
Arrhenius 1,2, 8, 9, 16, 25, 66, 141, 164
avidity 98
conductivity and dissociation in mixed solvents 157
constants of inversion 73
degrees of hydrolysis 91
electrolytic dissociation 3,4
equilibrium relations among electrolytes 69
heats of dissociation 140
temperature equation of 'dissociation constant 139
theory of isohydric solutions 62
and Fartjung , influence of pressure on dissociation 134
Walker, hydrolysis of salts of two weak ions 91,92
Association and ionization 154
Avidity 95
theory of 96
Baker, non-reactivity of dry substances. 162
Bases, and acids, neutralization of 58
definition of 5
influence of substituents on strength of 51
liberation from salts. 75
Basic salts, formation of, by hydrolysis up
Bassett , see Dorman 126
Baur , see Arrhenius 140
Beckmann 154
polymerization in solution 152
Bersch, Abegg , alkaline reaction by interaction of neutral compounds 117
BUtz, dissociation of caesium nitrate 127
and Meyer , conductivity of caesium nitrate 128
Bodlander 120
see Abegg. 127,161
Boiling-point, see RaouU .
Bredig , action of substituents on strength of bases 51
confirmations of the dilution law 45
hydrolysis p X
hydrolytic decomposition and ionic mobilities 86
inner complexes 125
mobilities of inorganic and organic ions 35
see Oshvald. **
INDEX.
167
PAGE
Bruhl, hydrated ions 153
unsaturated compounds and ionization 150
Buckingham, fluorescence of ions 13
Buff 3
Calculation of, absolute mobility * 31
electric mobility 32
equivalent conductivity at infinite dilution 34
maximum equivalent conductivity 32, 34
Cannizzaro , Kopp , and Keknle , abnormal vapor densities 7
Carbonates, solution of 115
Catalysis of cane-sugar by acids in the presence of neutral salts. 73
Cathion, slowest 35
Centner szwer, equivalent conductivities in HCN 149
Chemical nature and ionization tendency of the elements 159
Chlorine titration, Mohr's method 111
Volhard's method no
Clausius 3
Cohen , mixed solvents 157
Color of ionic solutions 12, 13
Complexes, formation of, Hittorj 125
inner 125
solubility, and electroaffinity 161
with S 0 2 in H a O solutions, Fox 153
Concentration chains, degree of ionization by means of 28
John 126
Concentration, changes in the vicinity of the electrode, Hittorj 29
high, and conductivity 132
in equivalents 20
in normals 20
' relation to conductivity. 43
sign 1
Concentrated solutions, dissociation of, Rudorj , Wolf 132
Concentrations, isohydric 64
Conductivity, and dilution constant 42
and salts, Hittorj 4
at infinite dilution 20, 22
equivalent 20
in benzonitrile and propionitrile, Schlundt, Lincoln, Dutoii.
149
i6S
INDEX.
page
Conductivity, in HCN, and dielectric constant, Centner sz-mr 149
in mixed solvents, Arrhenius 157
maximum equivalent, calculation of 32, 34
of isobydric solutions, Wakeman 66
of pnre fused salts 155
of pure water, Kohlrausch and Heyd'iveiller 56
of solid salts 157
specific 19
temperature and mobility 36
temperature coefficient of water 142
variation with concentration 43
Constant, hydrolytic 80
hydrolytic, of KCN, Shields 82
of dissociation, see Dissociation constant.
of inversion of adds in the presence of neutral salts . . 73
dielectric 148
Criticisms of ionic theory 14, 15
Current transport, mechanism of, within the solution 30
Davy 3
Decomposition voltages . 161
Degree of, dissociation from freezing-point and equivalent con
ductivity, Abegg 45
hydrolysis , ; , . 80
Shields , Walker gj-
ionization 24
by concentration chains, Jahn 28
Denison , see Steele ^4
Dibasic acids, dissociation of . 5D53
Dielectric constant, and dissociating power of solvents 147
of salts 4
Diffusion, chains, Nernst. j5
of electrolytes, Nernst . .
Dilution law, Ostivald, Starch . , van’t Hoff 39, 41, 130
and caesium nitrate .. t I2 g
concentrated solutions, Abegg , Rudorf. 3:32
confirmation of ^
exceptions I2I
theoretical basis, Roloff
INDEX
169
PAGE
Dissociating power of solvents 147
Dissociation, and i factor. 25
and temperature 135
and solvent 151
and medium 133
based on conductivity 156
in mixed solvents, Arrhenius , Cohen , Wolj 157
isotherm 131
non-electrolytic 152
of caesium nitrate according to conductivity and freezing-point. . . 128
of concentrated solutions, Rudorf , Wolf 132
of dibasic acids, Ostwald 51, 53
of mixed electrolytes 67, 69
of pure water. 56
of solute and association of solvent, Briihl , Dutoit 150
of water, variation with temperature, Kohlrausch and Heydweiller
60, 142
pressure influence on, Fanjung 134
Dissociation constant 40, 46
and chemical nature 47
and hydrolytic constant 82
degree of dissociation, equivalent conductivity 41, 44
influence upon, of substitution 47
of dibasic acids 53
of HCN, Walker 82
of RbN 0 3 127
physical significance of, Ostwald 46
strong electrolytes, Jahn , Kohlrausch , Rudolphi , van’t Hoff
123, 129
temperature equation of, Arrhenius 139
Dissociation constants 47,48
Dissociation degree 24
and dilution constant 41
by means of isohydric solutions 69
from freezing-point and equivalent conductivity, Abegg 45
Dissociation heat 136, 140
and pseudo acids 144
variability with temperature, Kohlrausch and Heydweiller 140
Donnan, Bassett , and Fox, inner complexes 126
110 INDEX.
PAGE
Diitoit, association of solvent and dissociation of solute 150
see Schliindt 149
Electroafimity, Abegg and Bodlander 161
solubility and complexes 161
Electrode, concentration change in the vicinity of 29
Electrolytes 2, 3, 4
amphoteric 160
anomaly of strong 121
dissociation constant of- strong, Jahn 123
dissociation of mixtures 69
equilibria among several 61
extremely weak 55
strong. 26
strong, equation for dissociation constant of, KohlrauscJi , Rudd phi,
van't Hoff. ’ 129
strong, obeying dilution law, Ostwald 124
weak 26
with negative temperature- coefficient of conductivity 140
Electrolytic, equilibrium relations, Arrhenius 61, 69
equilibria, heterogeneous 105
mobilities, Kohlrausch 3 2 j33
Electrolytic dissociation, see Dissociation, Arrhenius 4
fundamental conceptions of the theory 1
Elements, capacity for forming positive and negative ions 159
v. Ende 120
Energy, ionic consumption of, during electrolysis 3
Equation, a and i 25
a and A 24
dissociation constant, strong electrolytes, Kohlrausch , Rudolphi ,
% vanH Hoff 129
of Jahn - 123
of van 1 ! Hoff 59
Equilibria, among ions 37
among mixtures of electrolytes of equal strengths with common ions 74
among several electrolytes 61
heterogeneous, and hydrolysis 119
heterogeneous electrolytic 105
Equilibria in the hydrolysis of KCN 78
INDEX.
171
PAGE
Equilibrium of hydration 17
Equivalent conductivity (A) 20
degree of dissociation, dissociation constant 44
freezing-point, degree of dissociation 45
maximum, calculation of 32, 34
Euler , hydration of halogen ions 35
Fanfung , pressure and dissociation 134
Faraday / 3, 14
F, unit electrochemical quantity of electricity 14, 21
law of 14
Fluorescence of ions 13
Fox , complexes with S 0 2 in aqueous solutions 153
see Denman 126
Freezing-point, equivalent conductivity and degree of dissociation 45
see Raoult.
Goodwin 1 19
testing of solubility law : 107
Guinchard, dissociation constants of violuric acid and oximido-oxa-
zolon, variation with temperature 144
Halogens, hydration of, Euler 33
Hantzsch 160
isomers of phosphorous acid 146
pseudo acids 144
Heat of dissociation, and isomeric forms 145
Arrhenius , Baur , Thomsen 140
methods of determining 136
Heat of neutralization, methods of determining 138
Hess 39
Thomsen 137
Helmholtz 3
Hess. 60
heat of neutralization 59
thermoneutrality of salts 60
Heterogeneous electrolytic equilibria 105
Heydweiller i see Kohlrausch. 56,60, 140, 155
INDEX . .
172
PAGE
Hiitorf 3, 13
apportionment of the ions in transporting current 29
determination of nature of ions 4
electric conduction of salts . 4
formation of inner complexes 125
ratio of rates of migration of opposite ions 30
van't Hoff , see under V.
Holborn , see Kohlrausch 45
Hydrate, equilibrium 17
theory 16
theory and i factor 18
Hydrates, ionic * 126, 127
H} r dration, and mobility of inorganic ions 35
of the halogen ions, Eider 35
Hydrogen ions, characteristic reactions of 5
in organic compounds, conditions for production of 51
Hydrogen sulphide, ionization of. Walker 112
Hydrolysis 76
an ionic reaction, Kovalevsky 162
and heterogeneous equilibria up
and precipitation 95, 143
and water constant 142
degree of 80
degree of, Bredig, Shields, Walker p X
of KCN, Shields g 2
of salts of two weak ions 89
outward recognition 84
quantitative relations of, Ley p 2
reduction of
Hydrolytic, decomposition X 4
relations from the side of products of hydrolysis 95
Hydrolytic constant 80
and dissociation constant g 2
of oxides II4
Hydrolytic constants. Walker 84
Hydroxides, precipitation of, and hydrolysis !43
solubility of II4
Hydroxyl ions, characteristic reactions of 5
INDEX *73
PAGE
i factor . 8, 9
i factor, arid hydrate theory* 18
and number of ions, Taylor 18
osmotically and electrically measured 25
Immerwahr 1 19
Indicators 100
selection of 104
Influence of pressure and temperature on dissociation 134
Inversion constant for acids in presence of neutral salts, Arrhenius. 73
Ion, slowest anion 35
slowest cathion 35
Ionic, decomposition products, separation of 15
equivalent, quantity of electricity carried by 29
hydrates 126,127
mobility, temperature influence, Kohlrausch 33, 35
product 106
reactions 11,162
signs 1
theory, criticisms of 14, 15
Ionization, conception of 14
degree of 24
degree of, by concentration chains 28
history of, Roloff 3
see Dissociation-
tendency and chemical nature 159
tendency and solubility 161
Ions 3
and hydrolysis 92
and law of mass action 39
and periodic system 161
color of, Ostwald 12, 13
determination of nature of 4
energy consumption of, during electrolysis, Buff , Clausius ,
Helmholtz *. 3
equilibria among 37
fluorescence of, Buckingham 13
hydration of the halogens, Euler 35
hydrogen 5
hydrogen, discharged, Ostwald 16
i74
INDEX.
PAGE
Ions, hydrogen, in organic compounds 51
hydroxyl 6
independent nature of 14
inorganic, mobility and hydration of 35
law of Kohlrausch 21
mobility of, Bredig, Kohlrausch 29, 33, 35
mobility of organic 34
number of, normal value of osmotic pressure, and i factor 18, 19
positive and negative, from elements 159
reactions, and reaction velocity 162
transference numbers of 31
Isohydric concentrations 64
solutions, conductivity of 66
solutions, theory of, Arrhenius 62
Isomeric forms and heat of dissociation 145
Jaeger , solubility of HgO in H 2 F 2 114
Jahn 121, 129
degree of ionization by concentration chains 28
deviations from the dilution law 122
equation for E.M.F. of concentration chains 126
equation of 123
see Nernst 122
Kohlenberg 152
reactions in non-aqueous solutions 163
Kekule 7
Kohlrausch 34
electrolytic mobilities 33
equation for the dissociation constant 129
equivalent conductivity and dilution 20
hydrolysis of esters, an ionic reaction 162
influence of temperature on ionic mobility 33 7 35
law of the independent migration of ions 21, 22
relation of concentration to conductivity 43
and Ueydweiller 133
conductivity of pure water 56
conductivity temperature coefficient of water 141
variability of heat of dissociation and temperature, 140
INDEX. 175
PAGE
Kohlrausch and Heydweiller, water dissociation and temperature.. 60
and Holborn , confirmations of the dilution law 45
and Rose 120
Kopp . . 7
Kowalevsky, hydrolysis, an ionic reaction 162
Kuster and Tkeil 120
Law of, Faraday 14
Kohlrausch 21
mass action and caesium nitrate 127
mass action applied to ions 39
Raoult 6 , 7
solubility influence, Nernst 107
Le Chalelier, principle of 134, 135
“Lehrbuch der Allgemeinen Chemie,” Ostwald 2
Ley f quantitative relations of hydrolysis 92
Lincoln , see Schlundt 149
Mass-action law and ions 39
McCay 160
Mechanism of the current transport within the solution 30
Meyer , see Biltz 128
Migration law of ions, Kohlrausch 21
Migration of opposite ions, ratio of rates, Hittorf 30
Mixtures of salts. 10
Mobilities, electrolytic 33
Mobility, absolute, calculation of 31
conductivity, and temperature 36
electrolytic, calculation of 4 . . . 32
ionic, of hydrolyzed salts, Bredig 86
of ions 29
of ions, Bredig 35
of ions, temperature influence on 33, 35
of organic anions 34
Mohr's chlorine titration method no
Molar depression of the freezing-point of water 6
Mole 9
Molecular weight in solution, Raoult 2
Molecule number methods . .7
i7 6
INDEX.
PAGE
Nernst 17, 28, 106, 152, 163
electrolytic diffusion 16
see Ostwald 15, r6
solubility law 107
and Thomson's rule 147
and Jahn, interaction of ions and undissociated molecules 122
Neutral compounds, alkaline reaction of, by interaction „. 116
Neutralization, acids and bases 58
analogy to 76
by use of borax 88
heat, Hess 59
heats, Thomsen 137
Non-aqueous solutions 147
reactions in, Kohlenberg 163
Non-electrolytic dissociation 152
Noyes. . . . 120
inner complexes 125
solubility of thallous chloride 107
testing of solubility law 107
Organic anions, mobility of 34
Osmotic pressure, methods for determining molecular weight, see
Raonlt 2
normal value of, and number of ions 18
Ostwald , absorption spectra of permanganates 12
additive properties 1
avidity 96,98,99
Bredig , degree of dissociation, equivalent conductivity, disso-
ciation constant 44
confirmations of the dilution law 45
dilution law *. 39,41
dissociation of dibasic acids 51, 53
equivalent conductivity. 20
grouping electrolytes as to strength 25
ionization of water. . 57
“Lehrbuch der Allgem einen Chemie” 2
physical significance of the dissociation constant 46
solubility product - 106
strong electrolytes obeying dilution law .>■ 124 ‘ ,
INDEX .
177
PAGE
Ostwald, “Zeitschrift ftir physikalische Chemie ,, 2
and Nernst , discharged hydrogen ions 16
ionic charges 15
Oxide of mercury, solubility in H_F 2 114
Oxides, solubility of 114
Periodic system and ions 161
Phosphorous acid, isomers, Hantzsch 146
Polymerization, and ionization 150
in solution, Beckmann 152
Precipitates, conditions of formation 108
conversion of 109
solution of 1 15
Precipitation, by hydrolysis 95
of sulphides 112
Pressure, influence on dissociation, Fanjung 134
Principle of Le Chatelier 134
Pseudo acids, Hantzsch 144
Ramsay and Shields , polymerization of liquids 150
Raoult - 2,7,8,17
freezing-point, boiling-point, vapor-pressure methods 7, 151
law of 6, 7
molecular weight in solution 2
Ratio of the rates of migration of the opposite ions 30
Reaction velocity and ions 162
Reactions, ionic 11, 162
and ions. Baker 162
Reicher , see va?i't Hof 25, 41
Rolof, history of ionization 3
theoretical basis for dilution law 131
Rose f see Kohlrausch 120
Rudolphi , equation for dissociation constant of strong electrolytes. . 129
Rudorf , dissociation of concentrated solutions 132
Rule of Nernst and Thomson 147
Sackur 129
‘‘Salt,” conception of 4
Salt, mixtures : ig
178
INDEX.
PAGE
Salts, conductivity of pure 155
conductivity of solid, Warburg 157
conductivity temperature coefficients 36
dielectric constant of 155
formation of basic by hydrolysis 119
heats of dissociation of, Arrhenius . 141
hydrolysis of. Shields 87
ionic mobility of hydrolyzed, Bredig 86
of two weak ions, hydrolysis of 89
reactions of hydrolyzed 93
self-dissociation of 156
thermoneutrality of 60
“Sammlung chemischer und chemisch-technischer Vortrage” . . . . 2
Sclilundt , Lincoln , DiUoit , conductivities in benzo- and propionit- ile 149
Self -dissociation 155
of salts.
156
Sherrill.
120
Shields , degrees of hydrolysis 91
hydrolysis of salts 87
hydrolytic constant of KCN 82
ionization of water 57
see Ramsay 150
Sign, concentration 1
Signs, ionic 1
Solubility, electroaffinity, and complexes 161
law, Nernst , 107
of oxide of mercury in 114
of oxides and hydroxides 114
of sulphides 113
of thallous chloride, Noyes 107
product, Ostwald 106, 108
products, numerical values 120
Solution, of precipitates 115
polymerization in, Beckmann. 152
Solutions, additive nature of properties 12
dissociation of concentrated, Rudorf , Wolf 132
non-aqueous 147
theory of isohydric, Arrhenius 62
Solvent action of ammonia, 115
INDEX .
179
PAGE
Solvent, and dissociation 151
and solute, union of, Briihl , Walden .. . 153
Solvents, dissociating power of 147
electrolytic conductivity of pure, Walden 155
mixed 157
Sounding instrument, chemical in
Specific conductivity (x) 19
Specific gravity, additive nature of 13
Steele, inner complexes 125
and Denison , transference numbers of ions with greater valence
than one 34
Storch , dilution law 130
Strength, of acids, influence of substitution on 47
of bases, influence of substitution on 51
Strong electrolytes - 26
Substituents, position of, and strength of acids 50
Substitution, influence on dissociation constant 47, 51
Sulphides, grouping as to solubilities 113
precipitation of 112
Taylor , sodium mellitate and number of ions 18
Temperature, coefficients of conductivity of acids and salts 36
conductivity, and mobility 36
influence on dissociation 134
influence on ionic mobility. 33, 35
Theory, fundamental conceptions of electrolytic dissociation 1
hydrate 16
of avidity '. 96
of solution, van’t Hojf 2
Thermoneutrality. 136
of salts, Hess 60
Thiel , see Kiister : 120
Thomsen > 60
avidity 96
heats of neutralization 137
see Arrhenius 140
Thomson, see Nerns X47
Transference number, of the ion .■ 30
of ions with greater valence than one, Steele and Denison 34
Transport of current within the solution 30
i8o
INDEX .
PAGE
Valence, A begg. 161
Valson, additive nature of specific gravity 13
van’tHoff 2, 25,57, 131
dilution law of 130
dissociation constant equation 129
equation 59
i factor 8
solution theory 2, 7
and Reicher, degree of dissociation and dilution constant 41
Vapor densities, abnormal 7
Velocity of reaction and ions 162
Volhard , chlorine titration in
Voltages, decomposition 161
von Ende . 120
Wakeman?i y conductivity of isohydric solutions 66
W alden 45
electrolytic conductivity of pure solvents 155
union of solvent and solute 153
Walker. 87
degrees of hydrolysis qx
dissociation of HCN 82
hydrolytic constants * 84
ionization of hydrogen sulphide 112
see Arrhenius. qi
Warburg } conductivity of solid salts 137
Water constant and hydrolysis 142
Water, dissociation of, Ostwald , Shields , Wijs 57
dissociation, variation with temperature 60
electrolytic dissociation constant of 56
molar depression of freezing-point 6
temperature coefficient of conductivity, dissociation 142
Weak electrolytes 26
Wijs, ionisation of water 37
Wolf 157
avidity of weak acids 99
dissociation of concentrated solutions 132
mixed solvents 157
"Zeitschrift fur physikalische Chemie, ,T Ostwald 2
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